NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/12-shift.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 704 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(l(x))) → V(Xl(x))
M(V(c(x))) → V(Xc(x))
M(V(r(x))) → V(Xr(x))
Xa(a(x)) → a(Xa(x))
Xa(l(x)) → l(Xa(x))
Xa(c(x)) → c(Xa(x))
Xa(r(x)) → r(Xa(x))
Xl(a(x)) → a(Xl(x))
Xl(l(x)) → l(Xl(x))
Xl(c(x)) → c(Xl(x))
Xl(r(x)) → r(Xl(x))
Xc(a(x)) → a(Xc(x))
Xc(l(x)) → l(Xc(x))
Xc(c(x)) → c(Xc(x))
Xc(r(x)) → r(Xc(x))
Xr(a(x)) → a(Xr(x))
Xr(l(x)) → l(Xr(x))
Xr(c(x)) → c(Xr(x))
Xr(r(x)) → r(Xr(x))
Xa(E(x)) → a(E(x))
Xl(E(x)) → l(E(x))
Xc(E(x)) → c(E(x))
Xr(E(x)) → r(E(x))
W(V(x)) → R(L(x))
L(a(x)) → Ya(L(x))
L(l(x)) → Yl(L(x))
L(c(x)) → Yc(L(x))
L(r(x)) → Yr(L(x))
L(a(l(x))) → D(l(a(x)))
L(a(c(x))) → D(c(a(x)))
L(c(a(r(x)))) → D(r(a(x)))
L(l(r(a(a(x))))) → D(a(a(l(c(c(c(r(x))))))))
Ya(D(x)) → D(a(x))
Yl(D(x)) → D(l(x))
Yc(D(x)) → D(c(x))
Yr(D(x)) → D(r(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 c E → W V a c E

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

(2) NO