NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/dup01.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 149 ms)
↳2 NO

(0) Obligation:

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

Begin(a12(a34(a34(x)))) → Wait(Right1(x))
Begin(a34(a34(x))) → Wait(Right2(x))
Begin(a34(x)) → Wait(Right3(x))
Begin(a12(a45(a45(x)))) → Wait(Right4(x))
Begin(a45(a45(x))) → Wait(Right5(x))
Begin(a45(x)) → Wait(Right6(x))
Begin(a12(a56(a56(x)))) → Wait(Right7(x))
Begin(a56(a56(x))) → Wait(Right8(x))
Begin(a56(x)) → Wait(Right9(x))
Begin(a23(a45(a45(x)))) → Wait(Right10(x))
Begin(a45(a45(x))) → Wait(Right11(x))
Begin(a45(x)) → Wait(Right12(x))
Begin(a23(a56(a56(x)))) → Wait(Right13(x))
Begin(a56(a56(x))) → Wait(Right14(x))
Begin(a56(x)) → Wait(Right15(x))
Begin(a34(a56(a56(x)))) → Wait(Right16(x))
Begin(a56(a56(x))) → Wait(Right17(x))
Begin(a56(x)) → Wait(Right18(x))
Right1(a12(End(x))) → Left(a34(a34(a12(a12(End(x))))))
Right2(a12(a12(End(x)))) → Left(a34(a34(a12(a12(End(x))))))
Right3(a12(a12(a34(End(x))))) → Left(a34(a34(a12(a12(End(x))))))
Right4(a12(End(x))) → Left(a45(a45(a12(a12(End(x))))))
Right5(a12(a12(End(x)))) → Left(a45(a45(a12(a12(End(x))))))
Right6(a12(a12(a45(End(x))))) → Left(a45(a45(a12(a12(End(x))))))
Right7(a12(End(x))) → Left(a56(a56(a12(a12(End(x))))))
Right8(a12(a12(End(x)))) → Left(a56(a56(a12(a12(End(x))))))
Right9(a12(a12(a56(End(x))))) → Left(a56(a56(a12(a12(End(x))))))
Right10(a23(End(x))) → Left(a45(a45(a23(a23(End(x))))))
Right11(a23(a23(End(x)))) → Left(a45(a45(a23(a23(End(x))))))
Right12(a23(a23(a45(End(x))))) → Left(a45(a45(a23(a23(End(x))))))
Right13(a23(End(x))) → Left(a56(a56(a23(a23(End(x))))))
Right14(a23(a23(End(x)))) → Left(a56(a56(a23(a23(End(x))))))
Right15(a23(a23(a56(End(x))))) → Left(a56(a56(a23(a23(End(x))))))
Right16(a34(End(x))) → Left(a56(a56(a34(a34(End(x))))))
Right17(a34(a34(End(x)))) → Left(a56(a56(a34(a34(End(x))))))
Right18(a34(a34(a56(End(x))))) → Left(a56(a56(a34(a34(End(x))))))
Right1(a12(x)) → Aa12(Right1(x))
Right2(a12(x)) → Aa12(Right2(x))
Right3(a12(x)) → Aa12(Right3(x))
Right4(a12(x)) → Aa12(Right4(x))
Right5(a12(x)) → Aa12(Right5(x))
Right6(a12(x)) → Aa12(Right6(x))
Right7(a12(x)) → Aa12(Right7(x))
Right8(a12(x)) → Aa12(Right8(x))
Right9(a12(x)) → Aa12(Right9(x))
Right10(a12(x)) → Aa12(Right10(x))
Right11(a12(x)) → Aa12(Right11(x))
Right12(a12(x)) → Aa12(Right12(x))
Right13(a12(x)) → Aa12(Right13(x))
Right14(a12(x)) → Aa12(Right14(x))
Right15(a12(x)) → Aa12(Right15(x))
Right16(a12(x)) → Aa12(Right16(x))
Right17(a12(x)) → Aa12(Right17(x))
Right18(a12(x)) → Aa12(Right18(x))
Right1(a34(x)) → Aa34(Right1(x))
Right2(a34(x)) → Aa34(Right2(x))
Right3(a34(x)) → Aa34(Right3(x))
Right4(a34(x)) → Aa34(Right4(x))
Right5(a34(x)) → Aa34(Right5(x))
Right6(a34(x)) → Aa34(Right6(x))
Right7(a34(x)) → Aa34(Right7(x))
Right8(a34(x)) → Aa34(Right8(x))
Right9(a34(x)) → Aa34(Right9(x))
Right10(a34(x)) → Aa34(Right10(x))
Right11(a34(x)) → Aa34(Right11(x))
Right12(a34(x)) → Aa34(Right12(x))
Right13(a34(x)) → Aa34(Right13(x))
Right14(a34(x)) → Aa34(Right14(x))
Right15(a34(x)) → Aa34(Right15(x))
Right16(a34(x)) → Aa34(Right16(x))
Right17(a34(x)) → Aa34(Right17(x))
Right18(a34(x)) → Aa34(Right18(x))
Right1(a45(x)) → Aa45(Right1(x))
Right2(a45(x)) → Aa45(Right2(x))
Right3(a45(x)) → Aa45(Right3(x))
Right4(a45(x)) → Aa45(Right4(x))
Right5(a45(x)) → Aa45(Right5(x))
Right6(a45(x)) → Aa45(Right6(x))
Right7(a45(x)) → Aa45(Right7(x))
Right8(a45(x)) → Aa45(Right8(x))
Right9(a45(x)) → Aa45(Right9(x))
Right10(a45(x)) → Aa45(Right10(x))
Right11(a45(x)) → Aa45(Right11(x))
Right12(a45(x)) → Aa45(Right12(x))
Right13(a45(x)) → Aa45(Right13(x))
Right14(a45(x)) → Aa45(Right14(x))
Right15(a45(x)) → Aa45(Right15(x))
Right16(a45(x)) → Aa45(Right16(x))
Right17(a45(x)) → Aa45(Right17(x))
Right18(a45(x)) → Aa45(Right18(x))
Right1(a56(x)) → Aa56(Right1(x))
Right2(a56(x)) → Aa56(Right2(x))
Right3(a56(x)) → Aa56(Right3(x))
Right4(a56(x)) → Aa56(Right4(x))
Right5(a56(x)) → Aa56(Right5(x))
Right6(a56(x)) → Aa56(Right6(x))
Right7(a56(x)) → Aa56(Right7(x))
Right8(a56(x)) → Aa56(Right8(x))
Right9(a56(x)) → Aa56(Right9(x))
Right10(a56(x)) → Aa56(Right10(x))
Right11(a56(x)) → Aa56(Right11(x))
Right12(a56(x)) → Aa56(Right12(x))
Right13(a56(x)) → Aa56(Right13(x))
Right14(a56(x)) → Aa56(Right14(x))
Right15(a56(x)) → Aa56(Right15(x))
Right16(a56(x)) → Aa56(Right16(x))
Right17(a56(x)) → Aa56(Right17(x))
Right18(a56(x)) → Aa56(Right18(x))
Right1(a23(x)) → Aa23(Right1(x))
Right2(a23(x)) → Aa23(Right2(x))
Right3(a23(x)) → Aa23(Right3(x))
Right4(a23(x)) → Aa23(Right4(x))
Right5(a23(x)) → Aa23(Right5(x))
Right6(a23(x)) → Aa23(Right6(x))
Right7(a23(x)) → Aa23(Right7(x))
Right8(a23(x)) → Aa23(Right8(x))
Right9(a23(x)) → Aa23(Right9(x))
Right10(a23(x)) → Aa23(Right10(x))
Right11(a23(x)) → Aa23(Right11(x))
Right12(a23(x)) → Aa23(Right12(x))
Right13(a23(x)) → Aa23(Right13(x))
Right14(a23(x)) → Aa23(Right14(x))
Right15(a23(x)) → Aa23(Right15(x))
Right16(a23(x)) → Aa23(Right16(x))
Right17(a23(x)) → Aa23(Right17(x))
Right18(a23(x)) → Aa23(Right18(x))
Aa12(Left(x)) → Left(a12(x))
Aa34(Left(x)) → Left(a34(x))
Aa45(Left(x)) → Left(a45(x))
Aa56(Left(x)) → Left(a56(x))
Aa23(Left(x)) → Left(a23(x))
Wait(Left(x)) → Begin(x)
a12(a12(a34(a34(x)))) → a34(a34(a12(a12(x))))
a12(a12(a45(a45(x)))) → a45(a45(a12(a12(x))))
a12(a12(a56(a56(x)))) → a56(a56(a12(a12(x))))
a23(a23(a45(a45(x)))) → a45(a45(a23(a23(x))))
a23(a23(a56(a56(x)))) → a56(a56(a23(a23(x))))
a34(a34(a56(a56(x)))) → a56(a56(a34(a34(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 a56 a56 a34 a34 End → Wait Left a56 a56 a34 a34 End

Wait Left a56 a56 a34 a34 End → Wait Left a56 a56 a34 a34 End
by OverlapClosure OC 2
Wait Left a56 a56 → Wait Right17
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a56 a56 → Wait Right17
by original rule (OC 1)
Right17 a34 a34 End → Left a56 a56 a34 a34 End
by original rule (OC 1)

(2) NO