NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z072-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2695 ms)
↳2 NO

(0) Obligation:

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

begin(end(x)) → rewrite(end(x))
begin(a(x)) → rotate(cut(Ca(guess(x))))
begin(l(x)) → rotate(cut(Cl(guess(x))))
begin(r(x)) → rotate(cut(Cr(guess(x))))
begin(b(x)) → rotate(cut(Cb(guess(x))))
guess(a(x)) → Ca(guess(x))
guess(l(x)) → Cl(guess(x))
guess(r(x)) → Cr(guess(x))
guess(b(x)) → Cb(guess(x))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(l(x)) → moveleft(Bl(wait(x)))
guess(r(x)) → moveleft(Br(wait(x)))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(end(x)) → finish(end(x))
Ca(moveleft(Ba(x))) → moveleft(Ba(Aa(x)))
Cl(moveleft(Ba(x))) → moveleft(Ba(Al(x)))
Cr(moveleft(Ba(x))) → moveleft(Ba(Ar(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Ca(moveleft(Bl(x))) → moveleft(Bl(Aa(x)))
Cl(moveleft(Bl(x))) → moveleft(Bl(Al(x)))
Cr(moveleft(Bl(x))) → moveleft(Bl(Ar(x)))
Cb(moveleft(Bl(x))) → moveleft(Bl(Ab(x)))
Ca(moveleft(Br(x))) → moveleft(Br(Aa(x)))
Cl(moveleft(Br(x))) → moveleft(Br(Al(x)))
Cr(moveleft(Br(x))) → moveleft(Br(Ar(x)))
Cb(moveleft(Br(x))) → moveleft(Br(Ab(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
Cl(moveleft(Bb(x))) → moveleft(Bb(Al(x)))
Cr(moveleft(Bb(x))) → moveleft(Bb(Ar(x)))
Cb(moveleft(Bb(x))) → moveleft(Bb(Ab(x)))
cut(moveleft(Ba(x))) → Da(cut(goright(x)))
cut(moveleft(Bl(x))) → Dl(cut(goright(x)))
cut(moveleft(Br(x))) → Dr(cut(goright(x)))
cut(moveleft(Bb(x))) → Db(cut(goright(x)))
goright(Aa(x)) → Ca(goright(x))
goright(Al(x)) → Cl(goright(x))
goright(Ar(x)) → Cr(goright(x))
goright(Ab(x)) → Cb(goright(x))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(l(x))) → moveleft(Bl(wait(x)))
goright(wait(r(x))) → moveleft(Br(wait(x)))
goright(wait(b(x))) → moveleft(Bb(wait(x)))
goright(wait(end(x))) → finish(end(x))
Ca(finish(x)) → finish(a(x))
Cl(finish(x)) → finish(l(x))
Cr(finish(x)) → finish(r(x))
Cb(finish(x)) → finish(b(x))
cut(finish(x)) → finish2(x)
Da(finish2(x)) → finish2(a(x))
Dl(finish2(x)) → finish2(l(x))
Dr(finish2(x)) → finish2(r(x))
Db(finish2(x)) → finish2(b(x))
rotate(finish2(x)) → rewrite(x)
rewrite(a(l(x))) → begin(l(a(x)))
rewrite(r(a(a(x)))) → begin(a(a(r(x))))
rewrite(b(l(x))) → begin(b(a(r(x))))
rewrite(r(b(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 a l end → rewrite a l end

rewrite a l end → rewrite a l end
by OverlapClosure OC 3
rewrite a l end → rotate finish2 a l end
by OverlapClosure OC 3
rewrite a l end → rotate Da finish2 l end
by OverlapClosure OC 3
rewrite a l end → rotate Da cut finish l end
by OverlapClosure OC 3
rewrite a l end → rotate Da cut Cl finish end
by OverlapClosure OC 2
rewrite a l → rotate Da cut Cl goright wait
by OverlapClosure OC 3
rewrite a l → rotate Da cut goright Al wait
by OverlapClosure OC 3
rewrite a l → rotate cut moveleft Ba Al wait
by OverlapClosure OC 3
rewrite a l → rotate cut Cl moveleft Ba wait
by OverlapClosure OC 2
rewrite a l → rotate cut Cl guess a
by OverlapClosure OC 3
rewrite a l → begin l a
by original rule (OC 1)
begin l → rotate cut Cl guess
by original rule (OC 1)
guess a → moveleft Ba wait
by original rule (OC 1)
Cl moveleft Ba → moveleft Ba Al
by original rule (OC 1)
cut moveleft Ba → Da 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)
Da finish2 → finish2 a
by original rule (OC 1)
rotate finish2 → rewrite
by original rule (OC 1)

(2) NO