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-3.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 157 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(x)) → Wait(Right2(x))
Begin(b(a(x))) → Wait(Right3(x))
Begin(a(x)) → Wait(Right4(x))
Right1(a(End(x))) → Left(End(x))
Right2(a(End(x))) → Left(End(x))
Right3(b(End(x))) → Left(a(b(a(b(b(End(x)))))))
Right4(b(b(End(x)))) → Left(a(b(a(b(b(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(b(x)) → x
b(b(a(x))) → a(b(a(b(b(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 Right4
by original rule (OC 1)
Right4 b b End → Left a b b End
by OverlapClosure OC 3
Right4 b b End → Left a b a b b End
by original rule (OC 1)
a b →
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO