NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/07-oppelt08-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1223 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(R(x))) → V(XR(x))
M(V(b(x))) → V(Xb(x))
M(V(c(x))) → V(Xc(x))
M(V(L(x))) → V(XL(x))
M(V(a(x))) → V(Xa(x))
XR(R(x)) → R(XR(x))
XR(b(x)) → b(XR(x))
XR(c(x)) → c(XR(x))
XR(L(x)) → L(XR(x))
XR(a(x)) → a(XR(x))
Xb(R(x)) → R(Xb(x))
Xb(b(x)) → b(Xb(x))
Xb(c(x)) → c(Xb(x))
Xb(L(x)) → L(Xb(x))
Xb(a(x)) → a(Xb(x))
Xc(R(x)) → R(Xc(x))
Xc(b(x)) → b(Xc(x))
Xc(c(x)) → c(Xc(x))
Xc(L(x)) → L(Xc(x))
Xc(a(x)) → a(Xc(x))
XL(R(x)) → R(XL(x))
XL(b(x)) → b(XL(x))
XL(c(x)) → c(XL(x))
XL(L(x)) → L(XL(x))
XL(a(x)) → a(XL(x))
Xa(R(x)) → R(Xa(x))
Xa(b(x)) → b(Xa(x))
Xa(c(x)) → c(Xa(x))
Xa(L(x)) → L(Xa(x))
Xa(a(x)) → a(Xa(x))
XR(E(x)) → R(E(x))
Xb(E(x)) → b(E(x))
Xc(E(x)) → c(E(x))
XL(E(x)) → L(E(x))
Xa(E(x)) → a(E(x))
W(V(x)) → ZR(ZL(x))
ZL(R(x)) → YR(ZL(x))
ZL(b(x)) → Yb(ZL(x))
ZL(c(x)) → Yc(ZL(x))
ZL(L(x)) → YL(ZL(x))
ZL(a(x)) → Ya(ZL(x))
ZL(R(b(x))) → D(b(R(x)))
ZL(R(c(x))) → D(L(c(x)))
ZL(b(L(x))) → D(L(b(x)))
ZL(a(L(x))) → D(a(b(R(x))))
YR(D(x)) → D(R(x))
Yb(D(x)) → D(b(x))
Yc(D(x)) → D(c(x))
YL(D(x)) → D(L(x))
Ya(D(x)) → D(a(x))
ZR(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 L E → W V b L E

W V b L E → W V b L E
by OverlapClosure OC 2
W V b L → W V b XL
by OverlapClosure OC 2
W V b L → W V XL b
by OverlapClosure OC 3
W V b L → B L b
by OverlapClosure OC 3
W V b L → ZR D L b
by OverlapClosure OC 2
W V → ZR ZL
by original rule (OC 1)
ZL b L → D L b
by original rule (OC 1)
ZR D → B
by original rule (OC 1)
B L → W V XL
by OverlapClosure OC 2
B → W M V
by original rule (OC 1)
M V L → V XL
by original rule (OC 1)
XL b → b XL
by original rule (OC 1)
XL E → L E
by original rule (OC 1)

(2) NO