NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_06_SRS/secr1.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3697 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))
Right1(a(End(x))) → Left(b(b(b(b(End(x))))))
Right2(b(End(x))) → Left(a(a(a(a(End(x))))))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Wait(Left(x)) → Begin(x)
a(b(x)) → b(b(b(b(x))))
b(a(x)) → a(a(a(a(x))))
a(x) → x
b(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:
Wait Left a b b End → Wait Left a b b End

Wait Left a b b End → Wait Left a b b End
by OverlapClosure OC 3
Wait Left a b b End → Wait Left a b b b End
by OverlapClosure OC 3
Wait Left a b b End → Wait Aa Left b b b End
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a b b End → Wait Aa Left b b b End
by OverlapClosure OC 3
Begin a b b End → Wait Aa Left b b b b End
by OverlapClosure OC 2
Begin a b b End → Wait Aa Right1 a End
by OverlapClosure OC 3
Begin a b b End → Wait Right1 a a End
by OverlapClosure OC 3
Begin a b b End → Begin b a a End
by OverlapClosure OC 3
Begin a b b End → Wait Left b a a End
by OverlapClosure OC 3
Begin a b b End → Wait Ab Left a a End
by OverlapClosure OC 2
Begin a → Wait Right2
by original rule (OC 1)
Right2 b b End → Ab Left a a End
by OverlapClosure OC 2
Right2 b → Ab Right2
by original rule (OC 1)
Right2 b End → Left a a End
by OverlapClosure OC 3
Right2 b End → Left a a a End
by OverlapClosure OC 3
Right2 b End → Left a a a a End
by original rule (OC 1)
a →
by original rule (OC 1)
a →
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin b → Wait Right1
by original rule (OC 1)
Right1 a → Aa Right1
by original rule (OC 1)
Right1 a End → Left b b b b End
by original rule (OC 1)
b →
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
b →
by original rule (OC 1)

(2) NO