NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_05_SRS/aprove2-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3306 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(g(x))) → V(Xg(x))
M(V(h(x))) → V(Xh(x))
M(V(f(x))) → V(Xf(x))
M(V(s(x))) → V(Xs(x))
M(V(b(x))) → V(Xb(x))
M(V(a(x))) → V(Xa(x))
Xg(g(x)) → g(Xg(x))
Xg(h(x)) → h(Xg(x))
Xg(f(x)) → f(Xg(x))
Xg(s(x)) → s(Xg(x))
Xg(b(x)) → b(Xg(x))
Xg(a(x)) → a(Xg(x))
Xh(g(x)) → g(Xh(x))
Xh(h(x)) → h(Xh(x))
Xh(f(x)) → f(Xh(x))
Xh(s(x)) → s(Xh(x))
Xh(b(x)) → b(Xh(x))
Xh(a(x)) → a(Xh(x))
Xf(g(x)) → g(Xf(x))
Xf(h(x)) → h(Xf(x))
Xf(f(x)) → f(Xf(x))
Xf(s(x)) → s(Xf(x))
Xf(b(x)) → b(Xf(x))
Xf(a(x)) → a(Xf(x))
Xs(g(x)) → g(Xs(x))
Xs(h(x)) → h(Xs(x))
Xs(f(x)) → f(Xs(x))
Xs(s(x)) → s(Xs(x))
Xs(b(x)) → b(Xs(x))
Xs(a(x)) → a(Xs(x))
Xb(g(x)) → g(Xb(x))
Xb(h(x)) → h(Xb(x))
Xb(f(x)) → f(Xb(x))
Xb(s(x)) → s(Xb(x))
Xb(b(x)) → b(Xb(x))
Xb(a(x)) → a(Xb(x))
Xa(g(x)) → g(Xa(x))
Xa(h(x)) → h(Xa(x))
Xa(f(x)) → f(Xa(x))
Xa(s(x)) → s(Xa(x))
Xa(b(x)) → b(Xa(x))
Xa(a(x)) → a(Xa(x))
Xg(E(x)) → g(E(x))
Xh(E(x)) → h(E(x))
Xf(E(x)) → f(E(x))
Xs(E(x)) → s(E(x))
Xb(E(x)) → b(E(x))
Xa(E(x)) → a(E(x))
W(V(x)) → R(L(x))
L(g(x)) → Yg(L(x))
L(h(x)) → Yh(L(x))
L(f(x)) → Yf(L(x))
L(s(x)) → Ys(L(x))
L(b(x)) → Yb(L(x))
L(a(x)) → Ya(L(x))
L(g(h(x))) → D(g(f(s(x))))
L(f(s(s(s(x))))) → D(h(f(s(h(x)))))
L(f(h(x))) → D(h(f(s(h(x)))))
L(h(x)) → D(x)
L(f(f(s(s(x))))) → D(s(s(s(f(f(x))))))
L(b(a(x))) → D(a(b(x)))
L(a(a(a(x)))) → D(b(a(a(b(x)))))
L(b(b(b(b(x))))) → D(a(x))
Yg(D(x)) → D(g(x))
Yh(D(x)) → D(h(x))
Yf(D(x)) → D(f(x))
Ys(D(x)) → D(s(x))
Yb(D(x)) → D(b(x))
Ya(D(x)) → D(a(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 b a E → W V b a E

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

(2) NO