NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/08-oppelt08-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(a(L(x))) → Wait(Right1(x))
Begin(L(x)) → Wait(Right2(x))
Begin(L(x)) → Wait(Right3(x))
Right1(b(End(x))) → Left(L(a(L(X(b(a(b(b(End(x))))))))))
Right2(b(a(End(x)))) → Left(L(a(L(X(b(a(b(b(End(x))))))))))
Right3(b(End(x))) → Left(L(b(End(x))))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right1(L(x)) → AL(Right1(x))
Right2(L(x)) → AL(Right2(x))
Right3(L(x)) → AL(Right3(x))
Right1(X(x)) → AX(Right1(x))
Right2(X(x)) → AX(Right2(x))
Right3(X(x)) → AX(Right3(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
AL(Left(x)) → Left(L(x))
AX(Left(x)) → Left(X(x))
Wait(Left(x)) → Begin(x)
b(a(L(x))) → L(a(L(X(b(a(b(b(x))))))))
b(L(x)) → L(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:
Wait Left L b End → Wait Left L b End

Wait Left L b End → Wait Left L b End
by OverlapClosure OC 2
Wait Left L → Wait Right3
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin L → Wait Right3
by original rule (OC 1)
Right3 b End → Left L b End
by original rule (OC 1)

(2) NO