NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Trafo_06/dup17-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 110 ms)
↳2 NO

(0) Obligation:

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

Begin(a(a(a(x)))) → Wait(Right1(x))
Begin(a(a(x))) → Wait(Right2(x))
Begin(a(x)) → Wait(Right3(x))
Begin(b(a(a(x)))) → Wait(Right4(x))
Begin(a(a(x))) → Wait(Right5(x))
Begin(a(x)) → Wait(Right6(x))
Begin(b(b(b(c(c(x)))))) → Wait(Right7(x))
Begin(b(b(c(c(x))))) → Wait(Right8(x))
Begin(b(c(c(x)))) → Wait(Right9(x))
Begin(c(c(x))) → Wait(Right10(x))
Begin(c(x)) → Wait(Right11(x))
Begin(b(b(b(x)))) → Wait(Right12(x))
Begin(b(b(x))) → Wait(Right13(x))
Begin(b(x)) → Wait(Right14(x))
Begin(c(a(a(x)))) → Wait(Right15(x))
Begin(a(a(x))) → Wait(Right16(x))
Begin(a(x)) → Wait(Right17(x))
Right1(a(End(x))) → Left(b(b(End(x))))
Right2(a(a(End(x)))) → Left(b(b(End(x))))
Right3(a(a(a(End(x))))) → Left(b(b(End(x))))
Right4(b(End(x))) → Left(a(a(b(b(End(x))))))
Right5(b(b(End(x)))) → Left(a(a(b(b(End(x))))))
Right6(b(b(a(End(x))))) → Left(a(a(b(b(End(x))))))
Right7(b(End(x))) → Left(c(c(a(a(End(x))))))
Right8(b(b(End(x)))) → Left(c(c(a(a(End(x))))))
Right9(b(b(b(End(x))))) → Left(c(c(a(a(End(x))))))
Right10(b(b(b(b(End(x)))))) → Left(c(c(a(a(End(x))))))
Right11(b(b(b(b(c(End(x))))))) → Left(c(c(a(a(End(x))))))
Right12(b(End(x))) → Left(a(a(a(a(a(a(End(x))))))))
Right13(b(b(End(x)))) → Left(a(a(a(a(a(a(End(x))))))))
Right14(b(b(b(End(x))))) → Left(a(a(a(a(a(a(End(x))))))))
Right15(c(End(x))) → Left(b(b(a(a(c(c(End(x))))))))
Right16(c(c(End(x)))) → Left(b(b(a(a(c(c(End(x))))))))
Right17(c(c(a(End(x))))) → Left(b(b(a(a(c(c(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))
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))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(x))
Right5(c(x)) → Ac(Right5(x))
Right6(c(x)) → Ac(Right6(x))
Right7(c(x)) → Ac(Right7(x))
Right8(c(x)) → Ac(Right8(x))
Right9(c(x)) → Ac(Right9(x))
Right10(c(x)) → Ac(Right10(x))
Right11(c(x)) → Ac(Right11(x))
Right12(c(x)) → Ac(Right12(x))
Right13(c(x)) → Ac(Right13(x))
Right14(c(x)) → Ac(Right14(x))
Right15(c(x)) → Ac(Right15(x))
Right16(c(x)) → Ac(Right16(x))
Right17(c(x)) → Ac(Right17(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
a(a(a(a(x)))) → b(b(x))
b(b(a(a(x)))) → a(a(b(b(x))))
b(b(b(b(c(c(x)))))) → c(c(a(a(x))))
b(b(b(b(x)))) → a(a(a(a(a(a(x))))))
c(c(a(a(x)))) → b(b(a(a(c(c(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 a a b b End → Wait Left a a b b End

Wait Left a a b b End → Wait Left a a b b End
by OverlapClosure OC 2
Wait Left a a → Wait Right5
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a a → Wait Right5
by original rule (OC 1)
Right5 b b End → Left a a b b End
by original rule (OC 1)

(2) NO