NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z103-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1438 ms)
↳2 NO

(0) Obligation:

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

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

Begin b b b d End → Begin b b b d End
by OverlapClosure OC 3
Begin b b b d End → Begin a d End
by OverlapClosure OC 3
Begin b b b d End → Begin a c End
by OverlapClosure OC 3
Begin b b b d End → Wait Left a c End
by OverlapClosure OC 2
Begin b → Wait Right3
by original rule (OC 1)
Right3 b b d End → Left a c End
by OverlapClosure OC 3
Right3 b b d End → Left b d b End
by OverlapClosure OC 3
Right3 b b d End → Ab Left d b End
by OverlapClosure OC 2
Right3 b → Ab Right3
by original rule (OC 1)
Right3 b d End → Left d b End
by OverlapClosure OC 3
Right3 b d End → Left a d End
by OverlapClosure OC 3
Right3 b d End → Left a c End
by original rule (OC 1)
c → d
by original rule (OC 1)
a d → d b
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
b d b → a c
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
c → d
by original rule (OC 1)
a → b b b
by original rule (OC 1)

(2) NO