NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Bouchare_06/10-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 786 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))))
guess(b(x)) → Cb(guess(x))
guess(a(x)) → Ca(guess(x))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(end(x)) → finish(end(x))
Cb(moveleft(Bb(x))) → moveleft(Bb(Ab(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Ca(moveleft(Ba(x))) → moveleft(Ba(Aa(x)))
cut(moveleft(Bb(x))) → Db(cut(goright(x)))
cut(moveleft(Ba(x))) → Da(cut(goright(x)))
goright(Ab(x)) → Cb(goright(x))
goright(Aa(x)) → Ca(goright(x))
goright(wait(b(x))) → moveleft(Bb(wait(x)))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(end(x))) → finish(end(x))
Cb(finish(x)) → finish(b(x))
Ca(finish(x)) → finish(a(x))
cut(finish(x)) → finish2(x)
Db(finish2(x)) → finish2(b(x))
Da(finish2(x)) → finish2(a(x))
rotate(finish2(x)) → rewrite(x)
rewrite(b(b(b(x)))) → begin(a(a(b(x))))
rewrite(b(a(a(x)))) → begin(a(a(b(x))))
rewrite(a(a(x))) → begin(b(a(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 a a end → rewrite b a a end

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