NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/s6.srs-torpacyc2out-split.srs

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

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

(0) Obligation:

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

Begin(a34(x)) → Wait(Right1(x))
Begin(a45(x)) → Wait(Right2(x))
Begin(a56(x)) → Wait(Right3(x))
Begin(a45(x)) → Wait(Right4(x))
Begin(a56(x)) → Wait(Right5(x))
Begin(a56(x)) → Wait(Right6(x))
Right1(a12(End(x))) → Left(a34(a12(End(x))))
Right2(a12(End(x))) → Left(a45(a12(End(x))))
Right3(a12(End(x))) → Left(a56(a12(End(x))))
Right4(a23(End(x))) → Left(a45(a23(End(x))))
Right5(a23(End(x))) → Left(a56(a23(End(x))))
Right6(a34(End(x))) → Left(a56(a34(End(x))))
Right1(a12(x)) → Aa12(Right1(x))
Right2(a12(x)) → Aa12(Right2(x))
Right3(a12(x)) → Aa12(Right3(x))
Right4(a12(x)) → Aa12(Right4(x))
Right5(a12(x)) → Aa12(Right5(x))
Right6(a12(x)) → Aa12(Right6(x))
Right1(a34(x)) → Aa34(Right1(x))
Right2(a34(x)) → Aa34(Right2(x))
Right3(a34(x)) → Aa34(Right3(x))
Right4(a34(x)) → Aa34(Right4(x))
Right5(a34(x)) → Aa34(Right5(x))
Right6(a34(x)) → Aa34(Right6(x))
Right1(a45(x)) → Aa45(Right1(x))
Right2(a45(x)) → Aa45(Right2(x))
Right3(a45(x)) → Aa45(Right3(x))
Right4(a45(x)) → Aa45(Right4(x))
Right5(a45(x)) → Aa45(Right5(x))
Right6(a45(x)) → Aa45(Right6(x))
Right1(a56(x)) → Aa56(Right1(x))
Right2(a56(x)) → Aa56(Right2(x))
Right3(a56(x)) → Aa56(Right3(x))
Right4(a56(x)) → Aa56(Right4(x))
Right5(a56(x)) → Aa56(Right5(x))
Right6(a56(x)) → Aa56(Right6(x))
Right1(a23(x)) → Aa23(Right1(x))
Right2(a23(x)) → Aa23(Right2(x))
Right3(a23(x)) → Aa23(Right3(x))
Right4(a23(x)) → Aa23(Right4(x))
Right5(a23(x)) → Aa23(Right5(x))
Right6(a23(x)) → Aa23(Right6(x))
Aa12(Left(x)) → Left(a12(x))
Aa34(Left(x)) → Left(a34(x))
Aa45(Left(x)) → Left(a45(x))
Aa56(Left(x)) → Left(a56(x))
Aa23(Left(x)) → Left(a23(x))
Wait(Left(x)) → Begin(x)
a12(a34(x)) → a34(a12(x))
a12(a45(x)) → a45(a12(x))
a12(a56(x)) → a56(a12(x))
a23(a45(x)) → a45(a23(x))
a23(a56(x)) → a56(a23(x))
a34(a56(x)) → a56(a34(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 a56 a34 End → Wait Left a56 a34 End

Wait Left a56 a34 End → Wait Left a56 a34 End
by OverlapClosure OC 2
Wait Left a56 → Wait Right6
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a56 → Wait Right6
by original rule (OC 1)
Right6 a34 End → Left a56 a34 End
by original rule (OC 1)

(2) NO