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-343.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 810 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO