NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/09-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3243 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(s(x)) → rotate(cut(Cs(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(s(x)) → Cs(guess(x))
guess(b(x)) → Cb(guess(x))
guess(c(x)) → Cc(guess(x))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(s(x)) → moveleft(Bs(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)))
Cs(moveleft(Ba(x))) → moveleft(Ba(As(x)))
Cb(moveleft(Ba(x))) → moveleft(Ba(Ab(x)))
Cc(moveleft(Ba(x))) → moveleft(Ba(Ac(x)))
Ca(moveleft(Bs(x))) → moveleft(Bs(Aa(x)))
Cs(moveleft(Bs(x))) → moveleft(Bs(As(x)))
Cb(moveleft(Bs(x))) → moveleft(Bs(Ab(x)))
Cc(moveleft(Bs(x))) → moveleft(Bs(Ac(x)))
Ca(moveleft(Bb(x))) → moveleft(Bb(Aa(x)))
Cs(moveleft(Bb(x))) → moveleft(Bb(As(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)))
Cs(moveleft(Bc(x))) → moveleft(Bc(As(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(Bs(x))) → Ds(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(As(x)) → Cs(goright(x))
goright(Ab(x)) → Cb(goright(x))
goright(Ac(x)) → Cc(goright(x))
goright(wait(a(x))) → moveleft(Ba(wait(x)))
goright(wait(s(x))) → moveleft(Bs(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))
Cs(finish(x)) → finish(s(x))
Cb(finish(x)) → finish(b(x))
Cc(finish(x)) → finish(c(x))
cut(finish(x)) → finish2(x)
Da(finish2(x)) → finish2(a(x))
Ds(finish2(x)) → finish2(s(x))
Db(finish2(x)) → finish2(b(x))
Dc(finish2(x)) → finish2(c(x))
rotate(finish2(x)) → rewrite(x)
rewrite(a(s(x))) → begin(s(a(x)))
rewrite(b(a(b(s(x))))) → begin(a(b(s(a(x)))))
rewrite(b(a(b(b(x))))) → begin(c(s(x)))
rewrite(c(s(x))) → begin(a(b(a(b(x)))))
rewrite(a(b(a(a(x))))) → begin(b(a(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:
rewrite a s end → rewrite a s end

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