NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_05_SRS/matchbox1.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 551 ms)
↳2 NO

(0) Obligation:

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

Begin(e(x)) → Wait(Right1(x))
Begin(t(x)) → Wait(Right2(x))
Begin(r(x)) → Wait(Right3(x))
Right1(r(End(x))) → Left(w(r(End(x))))
Right2(i(End(x))) → Left(e(r(End(x))))
Right3(w(End(x))) → Left(i(t(End(x))))
Right1(r(x)) → Ar(Right1(x))
Right2(r(x)) → Ar(Right2(x))
Right3(r(x)) → Ar(Right3(x))
Right1(e(x)) → Ae(Right1(x))
Right2(e(x)) → Ae(Right2(x))
Right3(e(x)) → Ae(Right3(x))
Right1(w(x)) → Aw(Right1(x))
Right2(w(x)) → Aw(Right2(x))
Right3(w(x)) → Aw(Right3(x))
Right1(i(x)) → Ai(Right1(x))
Right2(i(x)) → Ai(Right2(x))
Right3(i(x)) → Ai(Right3(x))
Right1(t(x)) → At(Right1(x))
Right2(t(x)) → At(Right2(x))
Right3(t(x)) → At(Right3(x))
Ar(Left(x)) → Left(r(x))
Ae(Left(x)) → Left(e(x))
Aw(Left(x)) → Left(w(x))
Ai(Left(x)) → Left(i(x))
At(Left(x)) → Left(t(x))
Wait(Left(x)) → Begin(x)
r(e(x)) → w(r(x))
i(t(x)) → e(r(x))
w(r(x)) → i(t(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:
Begin e r End → Begin e r End

Begin e r End → Begin e r End
by OverlapClosure OC 3
Begin e r End → Wait Left e r End
by OverlapClosure OC 2
Begin e → Wait Right1
by original rule (OC 1)
Right1 r End → Left e r End
by OverlapClosure OC 3
Right1 r End → Left w r End
by original rule (OC 1)
w r → e r
by OverlapClosure OC 2
w r → i t
by original rule (OC 1)
i t → e r
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO