NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/beans1-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 116 ms)
↳2 NO

(0) Obligation:

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

Begin(2(1(x))) → Wait(Right1(x))
Begin(1(x)) → Wait(Right2(x))
Begin(2(1(x))) → Wait(Right3(x))
Begin(1(x)) → Wait(Right4(x))
Begin(2(1(x))) → Wait(Right5(x))
Begin(1(x)) → Wait(Right6(x))
Begin(2(0(x))) → Wait(Right7(x))
Begin(0(x)) → Wait(Right8(x))
Begin(2(R(x))) → Wait(Right9(x))
Begin(R(x)) → Wait(Right10(x))
Begin(2(0(x))) → Wait(Right11(x))
Begin(0(x)) → Wait(Right12(x))
Begin(2(0(x))) → Wait(Right13(x))
Begin(0(x)) → Wait(Right14(x))
Begin(2(R(x))) → Wait(Right15(x))
Begin(R(x)) → Wait(Right16(x))
Right1(1(End(x))) → Left(2(0(2(End(x)))))
Right2(1(2(End(x)))) → Left(2(0(2(End(x)))))
Right3(0(End(x))) → Left(1(0(2(End(x)))))
Right4(0(2(End(x)))) → Left(1(0(2(End(x)))))
Right5(L(End(x))) → Left(L(1(0(2(End(x))))))
Right6(L(2(End(x)))) → Left(L(1(0(2(End(x))))))
Right7(1(End(x))) → Left(2(0(1(End(x)))))
Right8(1(2(End(x)))) → Left(2(0(1(End(x)))))
Right9(1(End(x))) → Left(2(0(1(R(End(x))))))
Right10(1(2(End(x)))) → Left(2(0(1(R(End(x))))))
Right11(0(End(x))) → Left(1(0(1(End(x)))))
Right12(0(2(End(x)))) → Left(1(0(1(End(x)))))
Right13(L(End(x))) → Left(L(1(0(1(End(x))))))
Right14(L(2(End(x)))) → Left(L(1(0(1(End(x))))))
Right15(0(End(x))) → Left(1(0(1(R(End(x))))))
Right16(0(2(End(x)))) → Left(1(0(1(R(End(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))
Right13(1(x)) → A1(Right13(x))
Right14(1(x)) → A1(Right14(x))
Right15(1(x)) → A1(Right15(x))
Right16(1(x)) → A1(Right16(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))
Right13(2(x)) → A2(Right13(x))
Right14(2(x)) → A2(Right14(x))
Right15(2(x)) → A2(Right15(x))
Right16(2(x)) → A2(Right16(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))
Right13(0(x)) → A0(Right13(x))
Right14(0(x)) → A0(Right14(x))
Right15(0(x)) → A0(Right15(x))
Right16(0(x)) → A0(Right16(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))
Right13(L(x)) → AL(Right13(x))
Right14(L(x)) → AL(Right14(x))
Right15(L(x)) → AL(Right15(x))
Right16(L(x)) → AL(Right16(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))
Right13(R(x)) → AR(Right13(x))
Right14(R(x)) → AR(Right14(x))
Right15(R(x)) → AR(Right15(x))
Right16(R(x)) → AR(Right16(x))
A1(Left(x)) → Left(1(x))
A2(Left(x)) → Left(2(x))
A0(Left(x)) → Left(0(x))
AL(Left(x)) → Left(L(x))
AR(Left(x)) → Left(R(x))
Wait(Left(x)) → Begin(x)
1(2(1(x))) → 2(0(2(x)))
0(2(1(x))) → 1(0(2(x)))
L(2(1(x))) → L(1(0(2(x))))
1(2(0(x))) → 2(0(1(x)))
1(2(R(x))) → 2(0(1(R(x))))
0(2(0(x))) → 1(0(1(x)))
L(2(0(x))) → L(1(0(1(x))))
0(2(R(x))) → 1(0(1(R(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 1 0 2 End → Wait Left 1 0 2 End

Wait Left 1 0 2 End → Wait Left 1 0 2 End
by OverlapClosure OC 2
Wait Left 1 → Wait Right4
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin 1 → Wait Right4
by original rule (OC 1)
Right4 0 2 End → Left 1 0 2 End
by original rule (OC 1)

(2) NO