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-2-num-1.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1672 ms)
↳2 NO

(0) Obligation:

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

Begin(a(x)) → Wait(Right1(x))
Begin(a(b(x))) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Right1(a(End(x))) → Left(End(x))
Right2(a(End(x))) → Left(b(a(b(a(a(End(x)))))))
Right3(a(a(End(x)))) → Left(b(a(b(a(a(End(x)))))))
Right4(b(End(x))) → Left(End(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))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Wait(Left(x)) → Begin(x)
a(a(x)) → x
a(a(b(x))) → b(a(b(a(a(x)))))
b(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 b a b a a End → Wait Left b a b a a End

Wait Left b a b a a End → Wait Left b a b a a End
by OverlapClosure OC 2
Wait Left b → Wait Right3
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin b → Wait Right3
by original rule (OC 1)
Right3 a b a a End → Left b a b a a End
by OverlapClosure OC 3
Right3 a b a a End → Left a a b End
by OverlapClosure OC 3
Right3 a b a a End → Aa Left a b End
by OverlapClosure OC 3
Right3 a b a a End → Aa Left b b a b End
by OverlapClosure OC 2
Right3 a → Aa Right3
by original rule (OC 1)
Right3 b a a End → Left b b a b End
by OverlapClosure OC 3
Right3 b a a End → Ab Left b a b End
by OverlapClosure OC 2
Right3 b → Ab Right3
by original rule (OC 1)
Right3 a a End → Left b a b End
by OverlapClosure OC 3
Right3 a a End → Left b a b a a End
by original rule (OC 1)
a a →
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
b b →
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
a a b → b a b a a
by original rule (OC 1)

(2) NO