NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/06-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1662 ms)
↳2 NO

(0) Obligation:

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

Begin(a(b(x))) → Wait(Right1(x))
Begin(b(x)) → Wait(Right2(x))
Begin(b(a(x))) → Wait(Right3(x))
Begin(a(x)) → Wait(Right4(x))
Begin(a(x)) → Wait(Right5(x))
Begin(b(x)) → Wait(Right6(x))
Right1(b(End(x))) → Left(a(b(a(End(x)))))
Right2(b(a(End(x)))) → Left(a(b(a(End(x)))))
Right3(b(End(x))) → Left(b(b(b(End(x)))))
Right4(b(b(End(x)))) → Left(b(b(b(End(x)))))
Right5(c(End(x))) → Left(a(b(c(End(x)))))
Right6(c(End(x))) → Left(b(a(c(End(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))
Right6(b(x)) → Ab(Right6(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))
Right6(a(x)) → Aa(Right6(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))
Right6(c(x)) → Ac(Right6(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
b(a(b(x))) → a(b(a(x)))
b(b(a(x))) → b(b(b(x)))
c(a(x)) → a(b(c(x)))
c(b(x)) → b(a(c(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 b a b b End → Wait Left a b a b b End

Wait Left a b a b b End → Wait Left a b a b b End
by OverlapClosure OC 2
Wait Left a → Wait Right4
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a → Wait Right4
by original rule (OC 1)
Right4 b a b b End → Left a b a b b End
by OverlapClosure OC 3
Right4 b a b b End → Left b a b b b End
by OverlapClosure OC 3
Right4 b a b b End → Ab Left a b b b End
by OverlapClosure OC 2
Right4 b → Ab Right4
by original rule (OC 1)
Right4 a b b End → Left a b b b End
by OverlapClosure OC 3
Right4 a b b End → Aa Left b b b End
by OverlapClosure OC 2
Right4 a → Aa Right4
by original rule (OC 1)
Right4 b b End → Left b b b End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
b a b → a b a
by original rule (OC 1)

(2) NO