NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z094-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 502 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(f(x))) → V(Xf(x))
M(V(n(x))) → V(Xn(x))
M(V(c(x))) → V(Xc(x))
M(V(s(x))) → V(Xs(x))
Xf(f(x)) → f(Xf(x))
Xf(n(x)) → n(Xf(x))
Xf(c(x)) → c(Xf(x))
Xf(s(x)) → s(Xf(x))
Xn(f(x)) → f(Xn(x))
Xn(n(x)) → n(Xn(x))
Xn(c(x)) → c(Xn(x))
Xn(s(x)) → s(Xn(x))
Xc(f(x)) → f(Xc(x))
Xc(n(x)) → n(Xc(x))
Xc(c(x)) → c(Xc(x))
Xc(s(x)) → s(Xc(x))
Xs(f(x)) → f(Xs(x))
Xs(n(x)) → n(Xs(x))
Xs(c(x)) → c(Xs(x))
Xs(s(x)) → s(Xs(x))
Xf(E(x)) → f(E(x))
Xn(E(x)) → n(E(x))
Xc(E(x)) → c(E(x))
Xs(E(x)) → s(E(x))
W(V(x)) → R(L(x))
L(f(x)) → Yf(L(x))
L(n(x)) → Yn(L(x))
L(c(x)) → Yc(L(x))
L(s(x)) → Ys(L(x))
L(f(x)) → D(n(c(c(x))))
L(c(f(x))) → D(f(c(c(x))))
L(c(c(x))) → D(c(x))
L(n(s(x))) → D(f(s(s(x))))
L(n(f(x))) → D(f(n(x)))
Yf(D(x)) → D(f(x))
Yn(D(x)) → D(n(x))
Yc(D(x)) → D(c(x))
Ys(D(x)) → D(s(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 n f E → W V n f E

W V n f E → W V n f E
by OverlapClosure OC 2
W V n f → W V n Xf
by OverlapClosure OC 2
W V n f → W V Xf n
by OverlapClosure OC 3
W V n f → B f n
by OverlapClosure OC 3
W V n f → R D f n
by OverlapClosure OC 2
W V → R L
by original rule (OC 1)
L n f → D f n
by original rule (OC 1)
R D → B
by original rule (OC 1)
B f → W V Xf
by OverlapClosure OC 2
B → W M V
by original rule (OC 1)
M V f → V Xf
by original rule (OC 1)
Xf n → n Xf
by original rule (OC 1)
Xf E → f E
by original rule (OC 1)

(2) NO