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-498-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4953 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(a(x))) → D(b(a(c(x))))
L(b(b(x))) → D(a(a(x)))
L(c(b(x))) → D(a(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:
R D a a E → R D a a E

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

(2) NO