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

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

0 QTRS
↳1 NonTerminationProof (⇒, 479 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(w(x)) → Wait(Right3(x))
Begin(e(x)) → Wait(Right4(x))
Begin(r(x)) → Wait(Right5(x))
Begin(r(x)) → Wait(Right6(x))
Begin(i(t(e(r(x))))) → Wait(Right7(x))
Begin(t(e(r(x)))) → Wait(Right8(x))
Begin(e(r(x))) → Wait(Right9(x))
Begin(r(x)) → Wait(Right10(x))
Right1(r(End(x))) → Left(w(r(End(x))))
Right2(i(End(x))) → Left(e(r(End(x))))
Right3(e(End(x))) → Left(r(i(End(x))))
Right4(t(End(x))) → Left(r(e(End(x))))
Right5(w(End(x))) → Left(i(t(End(x))))
Right6(e(End(x))) → Left(e(w(End(x))))
Right7(r(End(x))) → Left(e(w(r(i(t(e(End(x))))))))
Right8(r(i(End(x)))) → Left(e(w(r(i(t(e(End(x))))))))
Right9(r(i(t(End(x))))) → Left(e(w(r(i(t(e(End(x))))))))
Right10(r(i(t(e(End(x)))))) → Left(e(w(r(i(t(e(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))
Right1(e(x)) → Ae(Right1(x))
Right2(e(x)) → Ae(Right2(x))
Right3(e(x)) → Ae(Right3(x))
Right4(e(x)) → Ae(Right4(x))
Right5(e(x)) → Ae(Right5(x))
Right6(e(x)) → Ae(Right6(x))
Right7(e(x)) → Ae(Right7(x))
Right8(e(x)) → Ae(Right8(x))
Right9(e(x)) → Ae(Right9(x))
Right10(e(x)) → Ae(Right10(x))
Right1(w(x)) → Aw(Right1(x))
Right2(w(x)) → Aw(Right2(x))
Right3(w(x)) → Aw(Right3(x))
Right4(w(x)) → Aw(Right4(x))
Right5(w(x)) → Aw(Right5(x))
Right6(w(x)) → Aw(Right6(x))
Right7(w(x)) → Aw(Right7(x))
Right8(w(x)) → Aw(Right8(x))
Right9(w(x)) → Aw(Right9(x))
Right10(w(x)) → Aw(Right10(x))
Right1(i(x)) → Ai(Right1(x))
Right2(i(x)) → Ai(Right2(x))
Right3(i(x)) → Ai(Right3(x))
Right4(i(x)) → Ai(Right4(x))
Right5(i(x)) → Ai(Right5(x))
Right6(i(x)) → Ai(Right6(x))
Right7(i(x)) → Ai(Right7(x))
Right8(i(x)) → Ai(Right8(x))
Right9(i(x)) → Ai(Right9(x))
Right10(i(x)) → Ai(Right10(x))
Right1(t(x)) → At(Right1(x))
Right2(t(x)) → At(Right2(x))
Right3(t(x)) → At(Right3(x))
Right4(t(x)) → At(Right4(x))
Right5(t(x)) → At(Right5(x))
Right6(t(x)) → At(Right6(x))
Right7(t(x)) → At(Right7(x))
Right8(t(x)) → At(Right8(x))
Right9(t(x)) → At(Right9(x))
Right10(t(x)) → At(Right10(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))
e(w(x)) → r(i(x))
t(e(x)) → r(e(x))
w(r(x)) → i(t(x))
e(r(x)) → e(w(x))
r(i(t(e(r(x))))) → e(w(r(i(t(e(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