NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-435.srs-torpacyc2out-split.srs

Termination w.r.t. Q of the given QTRS could be disproven:

0 QTRS
↳1 NonTerminationProof (⇒, 4917 ms)
↳2 NO

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin(a(b(x))) → Wait(Right1(x))
Begin(b(x)) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Right1(c(End(x))) → Left(a(a(c(End(x)))))
Right2(c(a(End(x)))) → Left(a(a(c(End(x)))))
Right3(c(End(x))) → Left(End(x))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
a(x) → b(b(c(x)))
c(a(b(x))) → a(a(c(x)))
c(b(x)) → x

Q is empty.

(1) NonTerminationProof (COMPLETE transformation)

We used the non-termination processor [OPPELT08] to show that the SRS problem is infinite.

Found the self-embedding DerivationStructure:
Begin a b b c End → Begin a b b c End

Begin a b b c End → Begin a b b c End
by OverlapClosure OC 3
Begin a b b c End → Wait Left a b b c End
by OverlapClosure OC 3
Begin a b b c End → Wait Aa Left b b c End
by OverlapClosure OC 3
Begin a b b c End → Wait Aa Aa Left End
by OverlapClosure OC 2
Begin a b b c End → Wait Aa Aa Right3 c End
by OverlapClosure OC 3
Begin a b b c End → Wait Aa Right3 a c End
by OverlapClosure OC 3
Begin a b b c End → Wait Right3 a a c End
by OverlapClosure OC 3
Begin a b b c End → Begin b a a c End
by OverlapClosure OC 3
Begin a b b c End → Wait Left b a a c End
by OverlapClosure OC 2
Begin a b → Wait Right1
by original rule (OC 1)
Right1 b c End → Left b a a c End
by OverlapClosure OC 3
Right1 b c End → Ab Left a a c End
by OverlapClosure OC 2
Right1 b → Ab Right1
by original rule (OC 1)
Right1 c End → Left a a c End
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin b → Wait Right3
by original rule (OC 1)
Right3 a → Aa Right3
by original rule (OC 1)
Right3 a → Aa Right3
by original rule (OC 1)
Right3 c End → Left End
by original rule (OC 1)
Aa Left → Left b b c
by OverlapClosure OC 2
Aa Left → Left a
by original rule (OC 1)
a → b b c
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO