NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z072-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 521 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(l(x))) → V(Xl(x))
M(V(r(x))) → V(Xr(x))
M(V(b(x))) → V(Xb(x))
Xa(a(x)) → a(Xa(x))
Xa(l(x)) → l(Xa(x))
Xa(r(x)) → r(Xa(x))
Xa(b(x)) → b(Xa(x))
Xl(a(x)) → a(Xl(x))
Xl(l(x)) → l(Xl(x))
Xl(r(x)) → r(Xl(x))
Xl(b(x)) → b(Xl(x))
Xr(a(x)) → a(Xr(x))
Xr(l(x)) → l(Xr(x))
Xr(r(x)) → r(Xr(x))
Xr(b(x)) → b(Xr(x))
Xb(a(x)) → a(Xb(x))
Xb(l(x)) → l(Xb(x))
Xb(r(x)) → r(Xb(x))
Xb(b(x)) → b(Xb(x))
Xa(E(x)) → a(E(x))
Xl(E(x)) → l(E(x))
Xr(E(x)) → r(E(x))
Xb(E(x)) → b(E(x))
W(V(x)) → R(L(x))
L(a(x)) → Ya(L(x))
L(l(x)) → Yl(L(x))
L(r(x)) → Yr(L(x))
L(b(x)) → Yb(L(x))
L(a(l(x))) → D(l(a(x)))
L(r(a(a(x)))) → D(a(a(r(x))))
L(b(l(x))) → D(b(a(r(x))))
L(r(b(x))) → D(l(b(x)))
Ya(D(x)) → D(a(x))
Yl(D(x)) → D(l(x))
Yr(D(x)) → D(r(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 l E → W V a l E

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

(2) NO