NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/examples/collection/ab-ba-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 250 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(b(x)) → rotate(cut(Cb(guess(x))))
guess(a(x)) → Ca(guess(x))
guess(b(x)) → Cb(guess(x))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(end(x)) → finish(end(x))
Ca(moveleft(Ba(x))) → moveleft(Ba(Aa(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
Cb(moveleft(Bb(x))) → moveleft(Bb(Ab(x)))
cut(moveleft(Ba(x))) → Da(cut(goright(x)))
cut(moveleft(Bb(x))) → Db(cut(goright(x)))
goright(Aa(x)) → Ca(goright(x))
goright(Ab(x)) → Cb(goright(x))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(b(x))) → moveleft(Bb(wait(x)))
goright(wait(end(x))) → finish(end(x))
Ca(finish(x)) → finish(a(x))
Cb(finish(x)) → finish(b(x))
cut(finish(x)) → finish2(x)
Da(finish2(x)) → finish2(a(x))
Db(finish2(x)) → finish2(b(x))
rotate(finish2(x)) → rewrite(x)
rewrite(a(b(x))) → begin(b(a(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:
rotate finish2 a b end → rotate finish2 a b end

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

(2) NO