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-549-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 6292 ms)
↳2 NO

(0) Obligation:

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

B(x) → W(M(V(x)))
M(x) → x
M(V(a(x))) → V(Xa(x))
M(V(b(x))) → V(Xb(x))
M(V(c(x))) → V(Xc(x))
Xa(a(x)) → a(Xa(x))
Xa(b(x)) → b(Xa(x))
Xa(c(x)) → c(Xa(x))
Xb(a(x)) → a(Xb(x))
Xb(b(x)) → b(Xb(x))
Xb(c(x)) → c(Xb(x))
Xc(a(x)) → a(Xc(x))
Xc(b(x)) → b(Xc(x))
Xc(c(x)) → c(Xc(x))
Xa(E(x)) → a(E(x))
Xb(E(x)) → b(E(x))
Xc(E(x)) → c(E(x))
W(V(x)) → R(L(x))
L(a(x)) → Ya(L(x))
L(b(x)) → Yb(L(x))
L(c(x)) → Yc(L(x))
L(a(b(x))) → D(x)
L(a(c(x))) → D(b(c(a(a(x)))))
L(c(b(x))) → D(a(c(x)))
Ya(D(x)) → D(a(x))
Yb(D(x)) → D(b(x))
Yc(D(x)) → D(c(x))
R(D(x)) → B(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:
W V a a c E → W V a a c E

W V a a c E → W V a a c E
by OverlapClosure OC 2
W V a a c → W V a a Xc
by OverlapClosure OC 2
W V a a c → W V a Xc a
by OverlapClosure OC 3
W V a a c → W V Xc a a
by OverlapClosure OC 3
W V a a c → B c a a
by OverlapClosure OC 3
W V a a c → B a b c a a
by OverlapClosure OC 3
W V a a c → R D a b c a a
by OverlapClosure OC 2
W V → R L
by original rule (OC 1)
L a a c → D a b c a a
by OverlapClosure OC 3
L a a c → Ya D b c a a
by OverlapClosure OC 2
L a → Ya L
by original rule (OC 1)
L a c → D b c a a
by original rule (OC 1)
Ya D → D a
by original rule (OC 1)
R D → B
by original rule (OC 1)
B a b → B
by OverlapClosure OC 2
B → W V
by OverlapClosure OC 3
B → W M V
by original rule (OC 1)
M →
by original rule (OC 1)
W V a b → B
by OverlapClosure OC 2
W V a b → R D
by OverlapClosure OC 2
W V → R L
by original rule (OC 1)
L a b → D
by original rule (OC 1)
R D → B
by original rule (OC 1)
B c → W V Xc
by OverlapClosure OC 2
B → W M V
by original rule (OC 1)
M V c → V Xc
by original rule (OC 1)
Xc a → a Xc
by original rule (OC 1)
Xc a → a Xc
by original rule (OC 1)
Xc E → c E
by original rule (OC 1)

(2) NO