NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/un05.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4662 ms)
↳2 NO

(0) Obligation:

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

Begin(b(b(b(x)))) → Wait(Right1(x))
Begin(b(b(x))) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Begin(a(b(b(a(b(x)))))) → Wait(Right4(x))
Begin(b(b(a(b(x))))) → Wait(Right5(x))
Begin(b(a(b(x)))) → Wait(Right6(x))
Begin(a(b(x))) → Wait(Right7(x))
Begin(b(x)) → Wait(Right8(x))
Right1(b(End(x))) → Left(b(b(b(a(b(End(x)))))))
Right2(b(b(End(x)))) → Left(b(b(b(a(b(End(x)))))))
Right3(b(b(b(End(x))))) → Left(b(b(b(a(b(End(x)))))))
Right4(b(End(x))) → Left(b(b(a(b(b(End(x)))))))
Right5(b(a(End(x)))) → Left(b(b(a(b(b(End(x)))))))
Right6(b(a(b(End(x))))) → Left(b(b(a(b(b(End(x)))))))
Right7(b(a(b(b(End(x)))))) → Left(b(b(a(b(b(End(x)))))))
Right8(b(a(b(b(a(End(x))))))) → Left(b(b(a(b(b(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))
Right7(b(x)) → Ab(Right7(x))
Right8(b(x)) → Ab(Right8(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))
Right7(a(x)) → Aa(Right7(x))
Right8(a(x)) → Aa(Right8(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Wait(Left(x)) → Begin(x)
b(b(b(b(x)))) → b(b(b(a(b(x)))))
b(a(b(b(a(b(x)))))) → b(b(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:
Begin b b b a b b End → Begin b b b a b b End

Begin b b b a b b End → Begin b b b a b b End
by OverlapClosure OC 3
Begin b b b a b b End → Wait Left b b b a b b End
by OverlapClosure OC 3
Begin b b b a b b End → Wait Ab Left b b a b b End
by OverlapClosure OC 2
Begin b b b a b b End → Wait Ab Right6 b a b End
by OverlapClosure OC 3
Begin b b b a b b End → Wait Right6 b b a b End
by OverlapClosure OC 3
Begin b b b a b b End → Begin b a b b b a b End
by OverlapClosure OC 3
Begin b b b a b b End → Wait Left b a b b b a b End
by OverlapClosure OC 2
Begin b b → Wait Right2
by original rule (OC 1)
Right2 b a b b End → Left b a b b b a b End
by OverlapClosure OC 3
Right2 b a b b End → Ab Left a b b b a b End
by OverlapClosure OC 2
Right2 b → Ab Right2
by original rule (OC 1)
Right2 a b b End → Left a b b b a b End
by OverlapClosure OC 3
Right2 a b b End → Aa Left b b b a b End
by OverlapClosure OC 2
Right2 a → Aa Right2
by original rule (OC 1)
Right2 b b End → Left b b b a 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)
Wait Left → Begin
by original rule (OC 1)
Begin b a b → Wait Right6
by original rule (OC 1)
Right6 b → Ab Right6
by original rule (OC 1)
Right6 b a b End → Left b b a b b End
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO