NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/un07.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 641 ms)
↳2 NO

(0) Obligation:

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

Begin(b(x)) → Wait(Right1(x))
Begin(b(a(b(x)))) → Wait(Right2(x))
Begin(a(b(x))) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Begin(a(b(x))) → Wait(Right5(x))
Begin(b(x)) → Wait(Right6(x))
Begin(a(a(b(a(b(x)))))) → Wait(Right7(x))
Begin(a(b(a(b(x))))) → Wait(Right8(x))
Begin(b(a(b(x)))) → Wait(Right9(x))
Begin(a(b(x))) → Wait(Right10(x))
Begin(b(x)) → Wait(Right11(x))
Right1(b(End(x))) → Left(b(a(b(End(x)))))
Right2(b(End(x))) → Left(b(a(b(a(a(b(b(End(x)))))))))
Right3(b(b(End(x)))) → Left(b(a(b(a(a(b(b(End(x)))))))))
Right4(b(b(a(End(x))))) → Left(b(a(b(a(a(b(b(End(x)))))))))
Right5(b(End(x))) → Left(b(a(a(b(End(x))))))
Right6(b(a(End(x)))) → Left(b(a(a(b(End(x))))))
Right7(b(End(x))) → Left(b(b(End(x))))
Right8(b(a(End(x)))) → Left(b(b(End(x))))
Right9(b(a(a(End(x))))) → Left(b(b(End(x))))
Right10(b(a(a(b(End(x)))))) → Left(b(b(End(x))))
Right11(b(a(a(b(a(End(x))))))) → Left(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))
Right9(b(x)) → Ab(Right9(x))
Right10(b(x)) → Ab(Right10(x))
Right11(b(x)) → Ab(Right11(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))
Right9(a(x)) → Aa(Right9(x))
Right10(a(x)) → Aa(Right10(x))
Right11(a(x)) → Aa(Right11(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Wait(Left(x)) → Begin(x)
b(b(x)) → b(a(b(x)))
b(b(a(b(x)))) → b(a(b(a(a(b(b(x)))))))
b(a(b(x))) → b(a(a(b(x))))
b(a(a(b(a(b(x)))))) → 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:
Wait Left b a b b End → Wait Left b a b b End

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

(2) NO