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-335.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 998 ms)
↳2 NO

(0) Obligation:

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

Begin(a(x)) → Wait(Right1(x))
Begin(b(b(x))) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Right1(a(End(x))) → Left(a(b(a(c(End(x))))))
Right2(c(End(x))) → Left(a(End(x)))
Right3(c(b(End(x)))) → Left(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(x) → b(x)
a(a(x)) → a(b(a(c(x))))
c(b(b(x))) → 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:
Wait Left b b a c End → Wait Left b b a c End

Wait Left b b a c End → Wait Left b b a c End
by OverlapClosure OC 3
Wait Left b b a c End → Wait Left a b a c End
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin b b a c End → Wait Left a b a c End
by OverlapClosure OC 2
Begin b b → Wait Right2
by original rule (OC 1)
Right2 a c End → Left a b a c End
by OverlapClosure OC 3
Right2 a c End → Left a a End
by OverlapClosure OC 3
Right2 a c End → Aa Left a End
by OverlapClosure OC 2
Right2 a → Aa Right2
by original rule (OC 1)
Right2 c End → Left a End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
a a → a b a c
by original rule (OC 1)
a → b
by original rule (OC 1)

(2) NO