NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z073-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2825 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(x))) → begin(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 r a end → rewrite r a end

rewrite r a end → rewrite r a end
by OverlapClosure OC 3
rewrite r a end → rotate finish2 r a end
by OverlapClosure OC 3
rewrite r a end → rotate Dr finish2 a end
by OverlapClosure OC 3
rewrite r a end → rotate Dr cut finish a end
by OverlapClosure OC 3
rewrite r a end → rotate Dr cut Ca finish end
by OverlapClosure OC 2
rewrite r a → rotate Dr cut Ca goright wait
by OverlapClosure OC 3
rewrite r a → rotate Dr cut goright Aa wait
by OverlapClosure OC 3
rewrite r a → rotate cut moveleft Br Aa wait
by OverlapClosure OC 3
rewrite r a → rotate cut Ca moveleft Br wait
by OverlapClosure OC 2
rewrite r a → rotate cut Ca guess r
by OverlapClosure OC 3
rewrite r a → begin a r
by original rule (OC 1)
begin a → rotate cut Ca guess
by original rule (OC 1)
guess r → moveleft Br wait
by original rule (OC 1)
Ca moveleft Br → moveleft Br Aa
by original rule (OC 1)
cut moveleft Br → Dr cut goright
by original rule (OC 1)
goright Aa → Ca goright
by original rule (OC 1)
goright wait end → finish end
by original rule (OC 1)
Ca finish → finish a
by original rule (OC 1)
cut finish → finish2
by original rule (OC 1)
Dr finish2 → finish2 r
by original rule (OC 1)
rotate finish2 → rewrite
by original rule (OC 1)

(2) NO