NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z067-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 76 ms)
↳2 NO

(0) Obligation:

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

Begin(p(x)) → Wait(Right1(x))
Begin(Q(Q(x))) → Wait(Right2(x))
Begin(Q(x)) → Wait(Right3(x))
Begin(p(q(x))) → Wait(Right4(x))
Begin(q(x)) → Wait(Right5(x))
Begin(q(p(x))) → Wait(Right6(x))
Begin(p(x)) → Wait(Right7(x))
Begin(Q(x)) → Wait(Right8(x))
Begin(q(x)) → Wait(Right9(x))
Begin(P(x)) → Wait(Right10(x))
Begin(p(x)) → Wait(Right11(x))
Right1(p(End(x))) → Left(q(q(End(x))))
Right2(p(End(x))) → Left(Q(Q(p(End(x)))))
Right3(p(Q(End(x)))) → Left(Q(Q(p(End(x)))))
Right4(Q(End(x))) → Left(q(p(Q(End(x)))))
Right5(Q(p(End(x)))) → Left(q(p(Q(End(x)))))
Right6(q(End(x))) → Left(p(q(q(End(x)))))
Right7(q(q(End(x)))) → Left(p(q(q(End(x)))))
Right8(q(End(x))) → Left(End(x))
Right9(Q(End(x))) → Left(End(x))
Right10(p(End(x))) → Left(End(x))
Right11(P(End(x))) → Left(End(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))
Right9(P(x)) → AP(Right9(x))
Right10(P(x)) → AP(Right10(x))
Right11(P(x)) → AP(Right11(x))
Right1(Q(x)) → AQ(Right1(x))
Right2(Q(x)) → AQ(Right2(x))
Right3(Q(x)) → AQ(Right3(x))
Right4(Q(x)) → AQ(Right4(x))
Right5(Q(x)) → AQ(Right5(x))
Right6(Q(x)) → AQ(Right6(x))
Right7(Q(x)) → AQ(Right7(x))
Right8(Q(x)) → AQ(Right8(x))
Right9(Q(x)) → AQ(Right9(x))
Right10(Q(x)) → AQ(Right10(x))
Right11(Q(x)) → AQ(Right11(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))
Right9(p(x)) → Ap(Right9(x))
Right10(p(x)) → Ap(Right10(x))
Right11(p(x)) → Ap(Right11(x))
Right1(q(x)) → Aq(Right1(x))
Right2(q(x)) → Aq(Right2(x))
Right3(q(x)) → Aq(Right3(x))
Right4(q(x)) → Aq(Right4(x))
Right5(q(x)) → Aq(Right5(x))
Right6(q(x)) → Aq(Right6(x))
Right7(q(x)) → Aq(Right7(x))
Right8(q(x)) → Aq(Right8(x))
Right9(q(x)) → Aq(Right9(x))
Right10(q(x)) → Aq(Right10(x))
Right11(q(x)) → Aq(Right11(x))
AP(Left(x)) → Left(P(x))
AQ(Left(x)) → Left(Q(x))
Ap(Left(x)) → Left(p(x))
Aq(Left(x)) → Left(q(x))
Wait(Left(x)) → Begin(x)
P(x) → Q(Q(p(x)))
p(p(x)) → q(q(x))
p(Q(Q(x))) → Q(Q(p(x)))
Q(p(q(x))) → q(p(Q(x)))
q(q(p(x))) → p(q(q(x)))
q(Q(x)) → x
Q(q(x)) → x
p(P(x)) → x
P(p(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 q q End → Wait Left p q q End

Wait Left p q q End → Wait Left p q q End
by OverlapClosure OC 2
Wait Left p → Wait Right7
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin p → Wait Right7
by original rule (OC 1)
Right7 q q End → Left p q q End
by original rule (OC 1)

(2) NO