NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Bouchare_06/18-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3678 ms)
↳2 NO

(0) Obligation:

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

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

Wait Left b a a b b a End → Wait Left b a a b b a End
by OverlapClosure OC 2
Wait Left b a → Wait Right1
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin b a → Wait Right1
by original rule (OC 1)
Right1 a b b a End → Left b a a b b a End
by OverlapClosure OC 3
Right1 a b b a End → Left b a a a b a End
by OverlapClosure OC 3
Right1 a b b a End → Left b b b b a End
by OverlapClosure OC 3
Right1 a b b a End → Left b b a b a End
by OverlapClosure OC 3
Right1 a b b a End → Left a b a b a End
by OverlapClosure OC 3
Right1 a b b a End → Left a b b b b a End
by OverlapClosure OC 3
Right1 a b b a End → Aa Left b b b b a End
by OverlapClosure OC 2
Right1 a → Aa Right1
by original rule (OC 1)
Right1 b b a End → Left b b b b a End
by OverlapClosure OC 3
Right1 b b a End → Ab Left b b b a End
by OverlapClosure OC 2
Right1 b → Ab Right1
by original rule (OC 1)
Right1 b a End → Left b b b a End
by OverlapClosure OC 3
Right1 b a End → Ab Left b b a End
by OverlapClosure OC 2
Right1 b → Ab Right1
by original rule (OC 1)
Right1 a End → Left b b a End
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
b b b → b a
by original rule (OC 1)
a b a → b b a
by original rule (OC 1)
a b a → b b a
by original rule (OC 1)
b b → a a a
by original rule (OC 1)
a b a → b b a
by original rule (OC 1)

(2) NO