NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_06_SRS/jw3.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 92 ms)
↳2 NO

(0) Obligation:

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

Begin(b(b(x1))) → Wait(Right1(x1))
Begin(b(x1)) → Wait(Right2(x1))
Begin(P(x1)) → Wait(Right3(x1))
Begin(x(x1)) → Wait(Right4(x1))
Begin(P(x1)) → Wait(Right5(x1))
Begin(x(x1)) → Wait(Right6(x1))
Begin(a(x1)) → Wait(Right7(x1))
Right1(a(End(x1))) → Left(P(a(b(End(x1)))))
Right2(a(b(End(x1)))) → Left(P(a(b(End(x1)))))
Right3(a(End(x1))) → Left(P(a(x(End(x1)))))
Right4(a(End(x1))) → Left(x(a(End(x1))))
Right5(b(End(x1))) → Left(b(Q(End(x1))))
Right6(Q(End(x1))) → Left(a(Q(End(x1))))
Right7(Q(End(x1))) → Left(b(b(a(End(x1)))))
Right1(a(x1)) → Aa(Right1(x1))
Right2(a(x1)) → Aa(Right2(x1))
Right3(a(x1)) → Aa(Right3(x1))
Right4(a(x1)) → Aa(Right4(x1))
Right5(a(x1)) → Aa(Right5(x1))
Right6(a(x1)) → Aa(Right6(x1))
Right7(a(x1)) → Aa(Right7(x1))
Right1(b(x1)) → Ab(Right1(x1))
Right2(b(x1)) → Ab(Right2(x1))
Right3(b(x1)) → Ab(Right3(x1))
Right4(b(x1)) → Ab(Right4(x1))
Right5(b(x1)) → Ab(Right5(x1))
Right6(b(x1)) → Ab(Right6(x1))
Right7(b(x1)) → Ab(Right7(x1))
Right1(P(x1)) → AP(Right1(x1))
Right2(P(x1)) → AP(Right2(x1))
Right3(P(x1)) → AP(Right3(x1))
Right4(P(x1)) → AP(Right4(x1))
Right5(P(x1)) → AP(Right5(x1))
Right6(P(x1)) → AP(Right6(x1))
Right7(P(x1)) → AP(Right7(x1))
Right1(x(x1)) → Ax(Right1(x1))
Right2(x(x1)) → Ax(Right2(x1))
Right3(x(x1)) → Ax(Right3(x1))
Right4(x(x1)) → Ax(Right4(x1))
Right5(x(x1)) → Ax(Right5(x1))
Right6(x(x1)) → Ax(Right6(x1))
Right7(x(x1)) → Ax(Right7(x1))
Right1(Q(x1)) → AQ(Right1(x1))
Right2(Q(x1)) → AQ(Right2(x1))
Right3(Q(x1)) → AQ(Right3(x1))
Right4(Q(x1)) → AQ(Right4(x1))
Right5(Q(x1)) → AQ(Right5(x1))
Right6(Q(x1)) → AQ(Right6(x1))
Right7(Q(x1)) → AQ(Right7(x1))
Aa(Left(x1)) → Left(a(x1))
Ab(Left(x1)) → Left(b(x1))
AP(Left(x1)) → Left(P(x1))
Ax(Left(x1)) → Left(x(x1))
AQ(Left(x1)) → Left(Q(x1))
Wait(Left(x1)) → Begin(x1)
a(b(b(x1))) → P(a(b(x1)))
a(P(x1)) → P(a(x(x1)))
a(x(x1)) → x(a(x1))
b(P(x1)) → b(Q(x1))
Q(x(x1)) → a(Q(x1))
Q(a(x1)) → b(b(a(x1)))

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 x a End → Wait Left x a End

Wait Left x a End → Wait Left x a End
by OverlapClosure OC 2
Wait Left x → Wait Right4
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin x → Wait Right4
by original rule (OC 1)
Right4 a End → Left x a End
by original rule (OC 1)

(2) NO