NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_06_SRS/6-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 557 ms)
↳2 NO

(0) Obligation:

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

B(x) → W(M(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(b(x))))) → D(b(a(a(a(x)))))
L(b(a(b(a(x))))) → D(a(b(b(a(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 a a a b E → W V a a a b E

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

(2) NO