NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/14-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1093 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))))
begin(c(x)) → rotate(cut(Cc(guess(x))))
guess(a(x)) → Ca(guess(x))
guess(b(x)) → Cb(guess(x))
guess(c(x)) → Cc(guess(x))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(c(x)) → moveleft(Bc(wait(x)))
guess(end(x)) → finish(end(x))
Ca(moveleft(Ba(x))) → moveleft(Ba(Aa(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Cc(moveleft(Ba(x))) → moveleft(Ba(Ac(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
Cb(moveleft(Bb(x))) → moveleft(Bb(Ab(x)))
Cc(moveleft(Bb(x))) → moveleft(Bb(Ac(x)))
Ca(moveleft(Bc(x))) → moveleft(Bc(Aa(x)))
Cb(moveleft(Bc(x))) → moveleft(Bc(Ab(x)))
Cc(moveleft(Bc(x))) → moveleft(Bc(Ac(x)))
cut(moveleft(Ba(x))) → Da(cut(goright(x)))
cut(moveleft(Bb(x))) → Db(cut(goright(x)))
cut(moveleft(Bc(x))) → Dc(cut(goright(x)))
goright(Aa(x)) → Ca(goright(x))
goright(Ab(x)) → Cb(goright(x))
goright(Ac(x)) → Cc(goright(x))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(b(x))) → moveleft(Bb(wait(x)))
goright(wait(c(x))) → moveleft(Bc(wait(x)))
goright(wait(end(x))) → finish(end(x))
Ca(finish(x)) → finish(a(x))
Cb(finish(x)) → finish(b(x))
Cc(finish(x)) → finish(c(x))
cut(finish(x)) → finish2(x)
Da(finish2(x)) → finish2(a(x))
Db(finish2(x)) → finish2(b(x))
Dc(finish2(x)) → finish2(c(x))
rotate(finish2(x)) → rewrite(x)
rewrite(a(a(x))) → begin(b(a(b(x))))
rewrite(b(b(x))) → begin(a(c(b(x))))
rewrite(c(c(x))) → begin(c(b(a(x))))
rewrite(a(b(x))) → begin(b(a(x)))
rewrite(b(c(x))) → begin(c(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 b end → rewrite a b end

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

(2) NO