NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Bouchare_06/06-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4266 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO