NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/09-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 788 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(s(x))) → V(Xs(x))
M(V(b(x))) → V(Xb(x))
M(V(c(x))) → V(Xc(x))
Xa(a(x)) → a(Xa(x))
Xa(s(x)) → s(Xa(x))
Xa(b(x)) → b(Xa(x))
Xa(c(x)) → c(Xa(x))
Xs(a(x)) → a(Xs(x))
Xs(s(x)) → s(Xs(x))
Xs(b(x)) → b(Xs(x))
Xs(c(x)) → c(Xs(x))
Xb(a(x)) → a(Xb(x))
Xb(s(x)) → s(Xb(x))
Xb(b(x)) → b(Xb(x))
Xb(c(x)) → c(Xb(x))
Xc(a(x)) → a(Xc(x))
Xc(s(x)) → s(Xc(x))
Xc(b(x)) → b(Xc(x))
Xc(c(x)) → c(Xc(x))
Xa(E(x)) → a(E(x))
Xs(E(x)) → s(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(s(x)) → Ys(L(x))
L(b(x)) → Yb(L(x))
L(c(x)) → Yc(L(x))
L(a(s(x))) → D(s(a(x)))
L(b(a(b(s(x))))) → D(a(b(s(a(x)))))
L(b(a(b(b(x))))) → D(c(s(x)))
L(c(s(x))) → D(a(b(a(b(x)))))
L(a(b(a(a(x))))) → D(b(a(b(a(x)))))
Ya(D(x)) → D(a(x))
Ys(D(x)) → D(s(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 s E → W V a s E

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

(2) NO