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

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

0 QTRS
↳1 NonTerminationProof (⇒, 175 ms)
↳2 NO

(0) Obligation:

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

Begin(q0(1(x))) → Wait(Right1(x))
Begin(1(x)) → Wait(Right2(x))
Begin(q0(0(x))) → Wait(Right3(x))
Begin(0(x)) → Wait(Right4(x))
Begin(q1(1(x))) → Wait(Right5(x))
Begin(1(x)) → Wait(Right6(x))
Begin(q1(0(x))) → Wait(Right7(x))
Begin(0(x)) → Wait(Right8(x))
Begin(q1(x)) → Wait(Right9(x))
Begin(q2(x)) → Wait(Right10(x))
Begin(q2(x)) → Wait(Right11(x))
Right1(1(End(x))) → Left(0(1(q1(End(x)))))
Right2(1(q0(End(x)))) → Left(0(1(q1(End(x)))))
Right3(1(End(x))) → Left(0(0(q1(End(x)))))
Right4(1(q0(End(x)))) → Left(0(0(q1(End(x)))))
Right5(1(End(x))) → Left(1(1(q1(End(x)))))
Right6(1(q1(End(x)))) → Left(1(1(q1(End(x)))))
Right7(1(End(x))) → Left(1(0(q1(End(x)))))
Right8(1(q1(End(x)))) → Left(1(0(q1(End(x)))))
Right9(0(End(x))) → Left(q2(1(End(x))))
Right10(1(End(x))) → Left(q2(1(End(x))))
Right11(0(End(x))) → Left(0(q0(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))
Right1(q0(x)) → Aq0(Right1(x))
Right2(q0(x)) → Aq0(Right2(x))
Right3(q0(x)) → Aq0(Right3(x))
Right4(q0(x)) → Aq0(Right4(x))
Right5(q0(x)) → Aq0(Right5(x))
Right6(q0(x)) → Aq0(Right6(x))
Right7(q0(x)) → Aq0(Right7(x))
Right8(q0(x)) → Aq0(Right8(x))
Right9(q0(x)) → Aq0(Right9(x))
Right10(q0(x)) → Aq0(Right10(x))
Right11(q0(x)) → Aq0(Right11(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))
Right1(q1(x)) → Aq1(Right1(x))
Right2(q1(x)) → Aq1(Right2(x))
Right3(q1(x)) → Aq1(Right3(x))
Right4(q1(x)) → Aq1(Right4(x))
Right5(q1(x)) → Aq1(Right5(x))
Right6(q1(x)) → Aq1(Right6(x))
Right7(q1(x)) → Aq1(Right7(x))
Right8(q1(x)) → Aq1(Right8(x))
Right9(q1(x)) → Aq1(Right9(x))
Right10(q1(x)) → Aq1(Right10(x))
Right11(q1(x)) → Aq1(Right11(x))
Right1(q2(x)) → Aq2(Right1(x))
Right2(q2(x)) → Aq2(Right2(x))
Right3(q2(x)) → Aq2(Right3(x))
Right4(q2(x)) → Aq2(Right4(x))
Right5(q2(x)) → Aq2(Right5(x))
Right6(q2(x)) → Aq2(Right6(x))
Right7(q2(x)) → Aq2(Right7(x))
Right8(q2(x)) → Aq2(Right8(x))
Right9(q2(x)) → Aq2(Right9(x))
Right10(q2(x)) → Aq2(Right10(x))
Right11(q2(x)) → Aq2(Right11(x))
A1(Left(x)) → Left(1(x))
Aq0(Left(x)) → Left(q0(x))
A0(Left(x)) → Left(0(x))
Aq1(Left(x)) → Left(q1(x))
Aq2(Left(x)) → Left(q2(x))
Wait(Left(x)) → Begin(x)
1(q0(1(x))) → 0(1(q1(x)))
1(q0(0(x))) → 0(0(q1(x)))
1(q1(1(x))) → 1(1(q1(x)))
1(q1(0(x))) → 1(0(q1(x)))
0(q1(x)) → q2(1(x))
1(q2(x)) → q2(1(x))
0(q2(x)) → 0(q0(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 q2 1 End → Wait Left q2 1 End

Wait Left q2 1 End → Wait Left q2 1 End
by OverlapClosure OC 2
Wait Left q2 → Wait Right10
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin q2 → Wait Right10
by original rule (OC 1)
Right10 1 End → Left q2 1 End
by original rule (OC 1)

(2) NO