NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z071-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 91 ms)
↳2 NO

(0) Obligation:

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

Begin(p(x)) → Wait(Right1(x))
Begin(r(x)) → Wait(Right2(x))
Begin(P(P(x))) → Wait(Right3(x))
Begin(P(x)) → Wait(Right4(x))
Begin(P(x)) → Wait(Right5(x))
Begin(p(x)) → Wait(Right6(x))
Begin(R(x)) → Wait(Right7(x))
Begin(r(x)) → Wait(Right8(x))
Right1(r(End(x))) → Left(p(p(r(P(End(x))))))
Right2(r(End(x))) → Left(End(x))
Right3(r(End(x))) → Left(P(P(r(End(x)))))
Right4(r(P(End(x)))) → Left(P(P(r(End(x)))))
Right5(p(End(x))) → Left(End(x))
Right6(P(End(x))) → Left(End(x))
Right7(r(End(x))) → Left(End(x))
Right8(R(End(x))) → Left(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))
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))
Right1(p(x)) → Ap(Right1(x))
Right2(p(x)) → Ap(Right2(x))
Right3(p(x)) → Ap(Right3(x))
Right4(p(x)) → Ap(Right4(x))
Right5(p(x)) → Ap(Right5(x))
Right6(p(x)) → Ap(Right6(x))
Right7(p(x)) → Ap(Right7(x))
Right8(p(x)) → Ap(Right8(x))
Right1(P(x)) → AP(Right1(x))
Right2(P(x)) → AP(Right2(x))
Right3(P(x)) → AP(Right3(x))
Right4(P(x)) → AP(Right4(x))
Right5(P(x)) → AP(Right5(x))
Right6(P(x)) → AP(Right6(x))
Right7(P(x)) → AP(Right7(x))
Right8(P(x)) → AP(Right8(x))
AR(Left(x)) → Left(R(x))
Ar(Left(x)) → Left(r(x))
Ap(Left(x)) → Left(p(x))
AP(Left(x)) → Left(P(x))
Wait(Left(x)) → Begin(x)
R(x) → r(x)
r(p(x)) → p(p(r(P(x))))
r(r(x)) → x
r(P(P(x))) → P(P(r(x)))
p(P(x)) → x
P(p(x)) → x
r(R(x)) → x
R(r(x)) → 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 P P r End → Wait Left P P r End

Wait Left P P r End → Wait Left P P r End
by OverlapClosure OC 2
Wait Left P P → Wait Right3
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin P P → Wait Right3
by original rule (OC 1)
Right3 r End → Left P P r End
by original rule (OC 1)

(2) NO