NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/08-oppelt08-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3002 ms)
↳2 NO

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

begin(end(x)) → rewrite(end(x))
begin(b(x)) → rotate(cut(Cb(guess(x))))
begin(a(x)) → rotate(cut(Ca(guess(x))))
begin(L(x)) → rotate(cut(CL(guess(x))))
begin(X(x)) → rotate(cut(CX(guess(x))))
guess(b(x)) → Cb(guess(x))
guess(a(x)) → Ca(guess(x))
guess(L(x)) → CL(guess(x))
guess(X(x)) → CX(guess(x))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(L(x)) → moveleft(BL(wait(x)))
guess(X(x)) → moveleft(BX(wait(x)))
guess(end(x)) → finish(end(x))
Cb(moveleft(Bb(x))) → moveleft(Bb(Ab(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
CL(moveleft(Bb(x))) → moveleft(Bb(AL(x)))
CX(moveleft(Bb(x))) → moveleft(Bb(AX(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Ca(moveleft(Ba(x))) → moveleft(Ba(Aa(x)))
CL(moveleft(Ba(x))) → moveleft(Ba(AL(x)))
CX(moveleft(Ba(x))) → moveleft(Ba(AX(x)))
Cb(moveleft(BL(x))) → moveleft(BL(Ab(x)))
Ca(moveleft(BL(x))) → moveleft(BL(Aa(x)))
CL(moveleft(BL(x))) → moveleft(BL(AL(x)))
CX(moveleft(BL(x))) → moveleft(BL(AX(x)))
Cb(moveleft(BX(x))) → moveleft(BX(Ab(x)))
Ca(moveleft(BX(x))) → moveleft(BX(Aa(x)))
CL(moveleft(BX(x))) → moveleft(BX(AL(x)))
CX(moveleft(BX(x))) → moveleft(BX(AX(x)))
cut(moveleft(Bb(x))) → Db(cut(goright(x)))
cut(moveleft(Ba(x))) → Da(cut(goright(x)))
cut(moveleft(BL(x))) → DL(cut(goright(x)))
cut(moveleft(BX(x))) → DX(cut(goright(x)))
goright(Ab(x)) → Cb(goright(x))
goright(Aa(x)) → Ca(goright(x))
goright(AL(x)) → CL(goright(x))
goright(AX(x)) → CX(goright(x))
goright(wait(b(x))) → moveleft(Bb(wait(x)))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(L(x))) → moveleft(BL(wait(x)))
goright(wait(X(x))) → moveleft(BX(wait(x)))
goright(wait(end(x))) → finish(end(x))
Cb(finish(x)) → finish(b(x))
Ca(finish(x)) → finish(a(x))
CL(finish(x)) → finish(L(x))
CX(finish(x)) → finish(X(x))
cut(finish(x)) → finish2(x)
Db(finish2(x)) → finish2(b(x))
Da(finish2(x)) → finish2(a(x))
DL(finish2(x)) → finish2(L(x))
DX(finish2(x)) → finish2(X(x))
rotate(finish2(x)) → rewrite(x)
rewrite(b(a(L(x)))) → begin(L(a(L(X(b(a(b(b(x)))))))))
rewrite(b(L(x))) → begin(L(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:
rewrite b L end → rewrite b L end

rewrite b L end → rewrite b L end
by OverlapClosure OC 3
rewrite b L end → rotate finish2 b L end
by OverlapClosure OC 3
rewrite b L end → rotate Db finish2 L end
by OverlapClosure OC 3
rewrite b L end → rotate Db cut finish L end
by OverlapClosure OC 3
rewrite b L end → rotate Db cut CL finish end
by OverlapClosure OC 2
rewrite b L → rotate Db cut CL goright wait
by OverlapClosure OC 3
rewrite b L → rotate Db cut goright AL wait
by OverlapClosure OC 3
rewrite b L → rotate cut moveleft Bb AL wait
by OverlapClosure OC 3
rewrite b L → rotate cut CL moveleft Bb wait
by OverlapClosure OC 2
rewrite b L → rotate cut CL guess b
by OverlapClosure OC 3
rewrite b L → begin L b
by original rule (OC 1)
begin L → rotate cut CL guess
by original rule (OC 1)
guess b → moveleft Bb wait
by original rule (OC 1)
CL moveleft Bb → moveleft Bb AL
by original rule (OC 1)
cut moveleft Bb → Db cut goright
by original rule (OC 1)
goright AL → CL goright
by original rule (OC 1)
goright wait end → finish end
by original rule (OC 1)
CL finish → finish L
by original rule (OC 1)
cut finish → finish2
by original rule (OC 1)
Db finish2 → finish2 b
by original rule (OC 1)
rotate finish2 → rewrite
by original rule (OC 1)

(2) NO