NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/while1.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 328 ms)
↳2 NO

(0) Obligation:

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

Begin(2(x)) → Wait(Right1(x))
Begin(3(x)) → Wait(Right2(x))
Begin(1(x)) → Wait(Right3(x))
Begin(L(x)) → Wait(Right4(x))
Begin(L(x)) → Wait(Right5(x))
Begin(L(x)) → Wait(Right6(x))
Begin(b(x)) → Wait(Right7(x))
Begin(c(x)) → Wait(Right8(x))
Begin(c(1(x))) → Wait(Right9(x))
Begin(1(x)) → Wait(Right10(x))
Begin(c(0(x))) → Wait(Right11(x))
Begin(0(x)) → Wait(Right12(x))
Right1(R(End(x))) → Left(2(R(End(x))))
Right2(R(End(x))) → Left(3(R(End(x))))
Right3(R(End(x))) → Left(L(3(End(x))))
Right4(3(End(x))) → Left(L(3(End(x))))
Right5(2(End(x))) → Left(L(2(End(x))))
Right6(0(End(x))) → Left(2(R(End(x))))
Right7(R(End(x))) → Left(c(1(b(End(x)))))
Right8(3(End(x))) → Left(c(1(End(x))))
Right9(2(End(x))) → Left(c(0(R(1(End(x))))))
Right10(2(c(End(x)))) → Left(c(0(R(1(End(x))))))
Right11(2(End(x))) → Left(c(0(0(End(x)))))
Right12(2(c(End(x)))) → Left(c(0(0(End(x)))))
Right1(R(x)) → AR(Right1(x))
Right2(R(x)) → AR(Right2(x))
Right3(R(x)) → AR(Right3(x))
Right4(R(x)) → AR(Right4(x))
Right5(R(x)) → AR(Right5(x))
Right6(R(x)) → AR(Right6(x))
Right7(R(x)) → AR(Right7(x))
Right8(R(x)) → AR(Right8(x))
Right9(R(x)) → AR(Right9(x))
Right10(R(x)) → AR(Right10(x))
Right11(R(x)) → AR(Right11(x))
Right12(R(x)) → AR(Right12(x))
Right1(2(x)) → A2(Right1(x))
Right2(2(x)) → A2(Right2(x))
Right3(2(x)) → A2(Right3(x))
Right4(2(x)) → A2(Right4(x))
Right5(2(x)) → A2(Right5(x))
Right6(2(x)) → A2(Right6(x))
Right7(2(x)) → A2(Right7(x))
Right8(2(x)) → A2(Right8(x))
Right9(2(x)) → A2(Right9(x))
Right10(2(x)) → A2(Right10(x))
Right11(2(x)) → A2(Right11(x))
Right12(2(x)) → A2(Right12(x))
Right1(3(x)) → A3(Right1(x))
Right2(3(x)) → A3(Right2(x))
Right3(3(x)) → A3(Right3(x))
Right4(3(x)) → A3(Right4(x))
Right5(3(x)) → A3(Right5(x))
Right6(3(x)) → A3(Right6(x))
Right7(3(x)) → A3(Right7(x))
Right8(3(x)) → A3(Right8(x))
Right9(3(x)) → A3(Right9(x))
Right10(3(x)) → A3(Right10(x))
Right11(3(x)) → A3(Right11(x))
Right12(3(x)) → A3(Right12(x))
Right1(1(x)) → A1(Right1(x))
Right2(1(x)) → A1(Right2(x))
Right3(1(x)) → A1(Right3(x))
Right4(1(x)) → A1(Right4(x))
Right5(1(x)) → A1(Right5(x))
Right6(1(x)) → A1(Right6(x))
Right7(1(x)) → A1(Right7(x))
Right8(1(x)) → A1(Right8(x))
Right9(1(x)) → A1(Right9(x))
Right10(1(x)) → A1(Right10(x))
Right11(1(x)) → A1(Right11(x))
Right12(1(x)) → A1(Right12(x))
Right1(L(x)) → AL(Right1(x))
Right2(L(x)) → AL(Right2(x))
Right3(L(x)) → AL(Right3(x))
Right4(L(x)) → AL(Right4(x))
Right5(L(x)) → AL(Right5(x))
Right6(L(x)) → AL(Right6(x))
Right7(L(x)) → AL(Right7(x))
Right8(L(x)) → AL(Right8(x))
Right9(L(x)) → AL(Right9(x))
Right10(L(x)) → AL(Right10(x))
Right11(L(x)) → AL(Right11(x))
Right12(L(x)) → AL(Right12(x))
Right1(0(x)) → A0(Right1(x))
Right2(0(x)) → A0(Right2(x))
Right3(0(x)) → A0(Right3(x))
Right4(0(x)) → A0(Right4(x))
Right5(0(x)) → A0(Right5(x))
Right6(0(x)) → A0(Right6(x))
Right7(0(x)) → A0(Right7(x))
Right8(0(x)) → A0(Right8(x))
Right9(0(x)) → A0(Right9(x))
Right10(0(x)) → A0(Right10(x))
Right11(0(x)) → A0(Right11(x))
Right12(0(x)) → A0(Right12(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))
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))
AR(Left(x)) → Left(R(x))
A2(Left(x)) → Left(2(x))
A3(Left(x)) → Left(3(x))
A1(Left(x)) → Left(1(x))
AL(Left(x)) → Left(L(x))
A0(Left(x)) → Left(0(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
R(2(x)) → 2(R(x))
R(3(x)) → 3(R(x))
R(1(x)) → L(3(x))
3(L(x)) → L(3(x))
2(L(x)) → L(2(x))
0(L(x)) → 2(R(x))
R(b(x)) → c(1(b(x)))
3(c(x)) → c(1(x))
2(c(1(x))) → c(0(R(1(x))))
2(c(0(x))) → c(0(0(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 L 2 End → Wait Left L 2 End

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

(2) NO