NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/dup05-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 138 ms)
↳2 NO

(0) Obligation:

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

Begin(a(s(s(x)))) → Wait(Right1(x))
Begin(s(s(x))) → Wait(Right2(x))
Begin(s(x)) → Wait(Right3(x))
Begin(b(a(a(b(b(s(s(x)))))))) → Wait(Right4(x))
Begin(a(a(b(b(s(s(x))))))) → Wait(Right5(x))
Begin(a(b(b(s(s(x)))))) → Wait(Right6(x))
Begin(b(b(s(s(x))))) → Wait(Right7(x))
Begin(b(s(s(x)))) → Wait(Right8(x))
Begin(s(s(x))) → Wait(Right9(x))
Begin(s(x)) → Wait(Right10(x))
Begin(b(a(a(b(b(b(b(x)))))))) → Wait(Right11(x))
Begin(a(a(b(b(b(b(x))))))) → Wait(Right12(x))
Begin(a(b(b(b(b(x)))))) → Wait(Right13(x))
Begin(b(b(b(b(x))))) → Wait(Right14(x))
Begin(b(b(b(x)))) → Wait(Right15(x))
Begin(b(b(x))) → Wait(Right16(x))
Begin(b(x)) → Wait(Right17(x))
Begin(a(b(b(a(a(a(a(x)))))))) → Wait(Right18(x))
Begin(b(b(a(a(a(a(x))))))) → Wait(Right19(x))
Begin(b(a(a(a(a(x)))))) → Wait(Right20(x))
Begin(a(a(a(a(x))))) → Wait(Right21(x))
Begin(a(a(a(x)))) → Wait(Right22(x))
Begin(a(a(x))) → Wait(Right23(x))
Begin(a(x)) → Wait(Right24(x))
Right1(a(End(x))) → Left(s(s(a(a(End(x))))))
Right2(a(a(End(x)))) → Left(s(s(a(a(End(x))))))
Right3(a(a(s(End(x))))) → Left(s(s(a(a(End(x))))))
Right4(b(End(x))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right5(b(b(End(x)))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right6(b(b(a(End(x))))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right7(b(b(a(a(End(x)))))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right8(b(b(a(a(b(End(x))))))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right9(b(b(a(a(b(b(End(x)))))))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right10(b(b(a(a(b(b(s(End(x))))))))) → Left(a(a(b(b(s(s(a(a(End(x))))))))))
Right11(b(End(x))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right12(b(b(End(x)))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right13(b(b(a(End(x))))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right14(b(b(a(a(End(x)))))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right15(b(b(a(a(b(End(x))))))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right16(b(b(a(a(b(b(End(x)))))))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right17(b(b(a(a(b(b(b(End(x))))))))) → Left(a(a(b(b(a(a(b(b(End(x))))))))))
Right18(a(End(x))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right19(a(a(End(x)))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right20(a(a(b(End(x))))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right21(a(a(b(b(End(x)))))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right22(a(a(b(b(a(End(x))))))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right23(a(a(b(b(a(a(End(x)))))))) → Left(b(b(a(a(b(b(a(a(End(x))))))))))
Right24(a(a(b(b(a(a(a(End(x))))))))) → Left(b(b(a(a(b(b(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))
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))
Right12(a(x)) → Aa(Right12(x))
Right13(a(x)) → Aa(Right13(x))
Right14(a(x)) → Aa(Right14(x))
Right15(a(x)) → Aa(Right15(x))
Right16(a(x)) → Aa(Right16(x))
Right17(a(x)) → Aa(Right17(x))
Right18(a(x)) → Aa(Right18(x))
Right19(a(x)) → Aa(Right19(x))
Right20(a(x)) → Aa(Right20(x))
Right21(a(x)) → Aa(Right21(x))
Right22(a(x)) → Aa(Right22(x))
Right23(a(x)) → Aa(Right23(x))
Right24(a(x)) → Aa(Right24(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))
Right11(s(x)) → As(Right11(x))
Right12(s(x)) → As(Right12(x))
Right13(s(x)) → As(Right13(x))
Right14(s(x)) → As(Right14(x))
Right15(s(x)) → As(Right15(x))
Right16(s(x)) → As(Right16(x))
Right17(s(x)) → As(Right17(x))
Right18(s(x)) → As(Right18(x))
Right19(s(x)) → As(Right19(x))
Right20(s(x)) → As(Right20(x))
Right21(s(x)) → As(Right21(x))
Right22(s(x)) → As(Right22(x))
Right23(s(x)) → As(Right23(x))
Right24(s(x)) → As(Right24(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))
Right12(b(x)) → Ab(Right12(x))
Right13(b(x)) → Ab(Right13(x))
Right14(b(x)) → Ab(Right14(x))
Right15(b(x)) → Ab(Right15(x))
Right16(b(x)) → Ab(Right16(x))
Right17(b(x)) → Ab(Right17(x))
Right18(b(x)) → Ab(Right18(x))
Right19(b(x)) → Ab(Right19(x))
Right20(b(x)) → Ab(Right20(x))
Right21(b(x)) → Ab(Right21(x))
Right22(b(x)) → Ab(Right22(x))
Right23(b(x)) → Ab(Right23(x))
Right24(b(x)) → Ab(Right24(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(a(s(s(x)))) → s(s(a(a(x))))
b(b(a(a(b(b(s(s(x)))))))) → a(a(b(b(s(s(a(a(x))))))))
b(b(a(a(b(b(b(b(x)))))))) → a(a(b(b(a(a(b(b(x))))))))
a(a(b(b(a(a(a(a(x)))))))) → b(b(a(a(b(b(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 s s a a End → Wait Left s s a a End

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

(2) NO