NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/06-oppelt08-split.srs

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

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

(0) Obligation:

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

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

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

(2) NO