NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Gebhardt_06/07-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1768 ms)
↳2 NO

(0) Obligation:

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

Begin(0(0(0(x)))) → Wait(Right1(x))
Begin(0(0(x))) → Wait(Right2(x))
Begin(0(x)) → Wait(Right3(x))
Begin(0(1(0(x)))) → Wait(Right4(x))
Begin(1(0(x))) → Wait(Right5(x))
Begin(0(x)) → Wait(Right6(x))
Right1(0(End(x))) → Left(0(1(0(1(End(x))))))
Right2(0(0(End(x)))) → Left(0(1(0(1(End(x))))))
Right3(0(0(0(End(x))))) → Left(0(1(0(1(End(x))))))
Right4(1(End(x))) → Left(0(1(0(0(End(x))))))
Right5(1(0(End(x)))) → Left(0(1(0(0(End(x))))))
Right6(1(0(1(End(x))))) → Left(0(1(0(0(End(x))))))
Right1(0(x)) → A0(Right1(x))
Right2(0(x)) → A0(Right2(x))
Right3(0(x)) → A0(Right3(x))
Right4(0(x)) → A0(Right4(x))
Right5(0(x)) → A0(Right5(x))
Right6(0(x)) → A0(Right6(x))
Right1(1(x)) → A1(Right1(x))
Right2(1(x)) → A1(Right2(x))
Right3(1(x)) → A1(Right3(x))
Right4(1(x)) → A1(Right4(x))
Right5(1(x)) → A1(Right5(x))
Right6(1(x)) → A1(Right6(x))
A0(Left(x)) → Left(0(x))
A1(Left(x)) → Left(1(x))
Wait(Left(x)) → Begin(x)
0(0(0(0(x)))) → 0(1(0(1(x))))
1(0(1(0(x)))) → 0(1(0(0(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 0 1 0 0 1 End → Begin 0 1 0 0 1 End

Begin 0 1 0 0 1 End → Begin 0 1 0 0 1 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Wait Left 0 1 0 0 1 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Wait Left 1 0 1 0 1 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Wait A1 Left 0 1 0 1 End
by OverlapClosure OC 2
Begin 0 1 0 0 1 End → Wait A1 Right2 0 0 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Wait Right2 1 0 0 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Begin 0 0 1 0 0 End
by OverlapClosure OC 3
Begin 0 1 0 0 1 End → Wait Left 0 0 1 0 0 End
by OverlapClosure OC 2
Begin 0 1 0 → Wait Right4
by original rule (OC 1)
Right4 0 1 End → Left 0 0 1 0 0 End
by OverlapClosure OC 3
Right4 0 1 End → A0 Left 0 1 0 0 End
by OverlapClosure OC 2
Right4 0 → A0 Right4
by original rule (OC 1)
Right4 1 End → Left 0 1 0 0 End
by original rule (OC 1)
A0 Left → Left 0
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin 0 0 → Wait Right2
by original rule (OC 1)
Right2 1 → A1 Right2
by original rule (OC 1)
Right2 0 0 End → Left 0 1 0 1 End
by original rule (OC 1)
A1 Left → Left 1
by original rule (OC 1)
1 0 1 0 → 0 1 0 0
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO