NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/10-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2342 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))
Begin(c(x)) → Wait(Right4(x))
Begin(c(x)) → Wait(Right5(x))
Right1(a(End(x))) → Left(d(b(End(x))))
Right2(b(End(x))) → Left(a(d(End(x))))
Right3(b(d(End(x)))) → Left(a(d(End(x))))
Right4(b(End(x))) → Left(c(d(d(End(x)))))
Right5(a(End(x))) → Left(b(b(c(d(End(x))))))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right4(a(x)) → Aa(Right4(x))
Right5(a(x)) → Aa(Right5(x))
Right1(d(x)) → Ad(Right1(x))
Right2(d(x)) → Ad(Right2(x))
Right3(d(x)) → Ad(Right3(x))
Right4(d(x)) → Ad(Right4(x))
Right5(d(x)) → Ad(Right5(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Right5(b(x)) → Ab(Right5(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(x))
Right5(c(x)) → Ac(Right5(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)))
d(x) → x
a(x) → x
b(d(b(x))) → a(d(x))
b(c(x)) → c(d(d(x)))
a(c(x)) → b(b(c(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:
Wait Left b b b d End → Wait Left b b b d End

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

(2) NO