NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_07_size12/size-12-alpha-3-num-495.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 247 ms)
↳2 NO

(0) Obligation:

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

Begin(a(x)) → Wait(Right1(x))
Begin(c(x)) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Right1(a(End(x))) → Left(b(End(x)))
Right2(b(End(x))) → Left(a(End(x)))
Right3(c(End(x))) → Left(b(c(c(a(End(x))))))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
a(a(x)) → b(x)
b(c(x)) → a(x)
c(b(x)) → b(c(c(a(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 a c a End → Begin a c a End

Begin a c a End → Begin a c a End
by OverlapClosure OC 3
Begin a c a End → Begin b c c a End
by OverlapClosure OC 3
Begin a c a End → Begin c b End
by OverlapClosure OC 3
Begin a c a End → Wait Left c b End
by OverlapClosure OC 2
Begin a → Wait Right1
by original rule (OC 1)
Right1 c a End → Left c b End
by OverlapClosure OC 3
Right1 c a End → Ac Left b End
by OverlapClosure OC 2
Right1 c → Ac Right1
by original rule (OC 1)
Right1 a End → Left b End
by original rule (OC 1)
Ac Left → Left c
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
c b → b c c a
by original rule (OC 1)
b c → a
by original rule (OC 1)

(2) NO