NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/01-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 112 ms)
↳2 NO

(0) Obligation:

Q restricted rewrite system:
The TRS R consists of the following rules:

Begin(b(x)) → Wait(Right1(x))
Begin(a(x)) → Wait(Right2(x))
Begin(a(x)) → Wait(Right3(x))
Right1(a(End(x))) → Left(b(r(End(x))))
Right2(r(End(x))) → Left(d(r(End(x))))
Right3(d(End(x))) → Left(a(a(d(End(x)))))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right1(r(x)) → Ar(Right1(x))
Right2(r(x)) → Ar(Right2(x))
Right3(r(x)) → Ar(Right3(x))
Right1(d(x)) → Ad(Right1(x))
Right2(d(x)) → Ad(Right2(x))
Right3(d(x)) → Ad(Right3(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ar(Left(x)) → Left(r(x))
Ad(Left(x)) → Left(d(x))
Wait(Left(x)) → Begin(x)
a(b(x)) → b(r(x))
r(a(x)) → d(r(x))
r(x) → d(x)
d(a(x)) → a(a(d(x)))
d(x) → 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:
Wait Left a r End → Wait Left a r End

Wait Left a r End → Wait Left a r End
by OverlapClosure OC 3
Wait Left a r End → Wait Left d r End
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a r End → Wait Left d r End
by OverlapClosure OC 2
Begin a → Wait Right2
by original rule (OC 1)
Right2 r End → Left d r End
by original rule (OC 1)
d → a
by original rule (OC 1)

(2) NO