NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z106-rotate.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2762 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))))
begin(d(x)) → rotate(cut(Cd(guess(x))))
guess(a(x)) → Ca(guess(x))
guess(b(x)) → Cb(guess(x))
guess(c(x)) → Cc(guess(x))
guess(d(x)) → Cd(guess(x))
guess(a(x)) → moveleft(Ba(wait(x)))
guess(b(x)) → moveleft(Bb(wait(x)))
guess(c(x)) → moveleft(Bc(wait(x)))
guess(d(x)) → moveleft(Bd(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)))
Cd(moveleft(Ba(x))) → moveleft(Ba(Ad(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)))
Cd(moveleft(Bb(x))) → moveleft(Bb(Ad(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)))
Cd(moveleft(Bc(x))) → moveleft(Bc(Ad(x)))
Ca(moveleft(Bd(x))) → moveleft(Bd(Aa(x)))
Cb(moveleft(Bd(x))) → moveleft(Bd(Ab(x)))
Cc(moveleft(Bd(x))) → moveleft(Bd(Ac(x)))
Cd(moveleft(Bd(x))) → moveleft(Bd(Ad(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)))
cut(moveleft(Bd(x))) → Dd(cut(goright(x)))
goright(Aa(x)) → Ca(goright(x))
goright(Ab(x)) → Cb(goright(x))
goright(Ac(x)) → Cc(goright(x))
goright(Ad(x)) → Cd(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(d(x))) → moveleft(Bd(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))
Cd(finish(x)) → finish(d(x))
cut(finish(x)) → finish2(x)
Da(finish2(x)) → finish2(a(x))
Db(finish2(x)) → finish2(b(x))
Dc(finish2(x)) → finish2(c(x))
Dd(finish2(x)) → finish2(d(x))
rotate(finish2(x)) → rewrite(x)
rewrite(a(a(x))) → begin(b(b(b(x))))
rewrite(b(x)) → begin(c(c(d(x))))
rewrite(c(x)) → begin(d(d(d(x))))
rewrite(b(c(x))) → begin(c(b(x)))
rewrite(b(c(d(x)))) → begin(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 b c end → rewrite b c end

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