NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/beans2.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 40 ms)
↳2 NO

(0) Obligation:

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

Begin(a(a(x))) → Wait(Right1(x))
Begin(a(x)) → Wait(Right2(x))
Begin(a(x)) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Begin(a(a(x))) → Wait(Right5(x))
Begin(a(x)) → Wait(Right6(x))
Begin(R(x)) → Wait(Right7(x))
Right1(b(End(x))) → Left(a(b(c(End(x)))))
Right2(b(a(End(x)))) → Left(a(b(c(End(x)))))
Right3(c(End(x))) → Left(a(c(End(x))))
Right4(c(End(x))) → Left(b(a(End(x))))
Right5(L(End(x))) → Left(L(a(b(c(End(x))))))
Right6(L(a(End(x)))) → Left(L(a(b(c(End(x))))))
Right7(c(End(x))) → Left(b(a(R(End(x)))))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Right5(b(x)) → Ab(Right5(x))
Right6(b(x)) → Ab(Right6(x))
Right7(b(x)) → Ab(Right7(x))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right4(a(x)) → Aa(Right4(x))
Right5(a(x)) → Aa(Right5(x))
Right6(a(x)) → Aa(Right6(x))
Right7(a(x)) → Aa(Right7(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(x))
Right5(c(x)) → Ac(Right5(x))
Right6(c(x)) → Ac(Right6(x))
Right7(c(x)) → Ac(Right7(x))
Right1(L(x)) → AL(Right1(x))
Right2(L(x)) → AL(Right2(x))
Right3(L(x)) → AL(Right3(x))
Right4(L(x)) → AL(Right4(x))
Right5(L(x)) → AL(Right5(x))
Right6(L(x)) → AL(Right6(x))
Right7(L(x)) → AL(Right7(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))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Ac(Left(x)) → Left(c(x))
AL(Left(x)) → Left(L(x))
AR(Left(x)) → Left(R(x))
Wait(Left(x)) → Begin(x)
b(a(a(x))) → a(b(c(x)))
c(a(x)) → a(c(x))
c(b(x)) → b(a(x))
L(a(a(x))) → L(a(b(c(x))))
c(R(x)) → b(a(R(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 a c End → Wait Left a c End

Wait Left a c End → Wait Left a c End
by OverlapClosure OC 2
Wait Left a → Wait Right3
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a → Wait Right3
by original rule (OC 1)
Right3 c End → Left a c End
by original rule (OC 1)

(2) NO