NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z008.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 54 ms)
↳2 NO

(0) Obligation:

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

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

Wait Left s a End → Wait Left s a End
by OverlapClosure OC 2
Wait Left s → Wait Right1
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin s → Wait Right1
by original rule (OC 1)
Right1 a End → Left s a End
by original rule (OC 1)

(2) NO