NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/01-oppelt08.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 611 ms)
↳2 NO

(0) Obligation:

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

Begin(b(c(x))) → Wait(Right1(x))
Begin(c(x)) → Wait(Right2(x))
Begin(c(x)) → Wait(Right3(x))
Begin(a(b(x))) → Wait(Right4(x))
Begin(b(x)) → Wait(Right5(x))
Begin(a(c(x))) → Wait(Right6(x))
Begin(c(x)) → Wait(Right7(x))
Right1(a(End(x))) → Left(c(b(a(End(x)))))
Right2(a(b(End(x)))) → Left(c(b(a(End(x)))))
Right3(a(End(x))) → Left(a(a(d(a(End(x))))))
Right4(d(End(x))) → Left(b(a(d(End(x)))))
Right5(d(a(End(x)))) → Left(b(a(d(End(x)))))
Right6(d(End(x))) → Left(b(c(c(End(x)))))
Right7(d(a(End(x)))) → Left(b(c(c(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))
Right5(a(x)) → Aa(Right5(x))
Right6(a(x)) → Aa(Right6(x))
Right7(a(x)) → Aa(Right7(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))
Right5(b(x)) → Ab(Right5(x))
Right6(b(x)) → Ab(Right6(x))
Right7(b(x)) → Ab(Right7(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(x))
Right5(c(x)) → Ac(Right5(x))
Right6(c(x)) → Ac(Right6(x))
Right7(c(x)) → Ac(Right7(x))
Right1(d(x)) → Ad(Right1(x))
Right2(d(x)) → Ad(Right2(x))
Right3(d(x)) → Ad(Right3(x))
Right4(d(x)) → Ad(Right4(x))
Right5(d(x)) → Ad(Right5(x))
Right6(d(x)) → Ad(Right6(x))
Right7(d(x)) → Ad(Right7(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Ad(Left(x)) → Left(d(x))
Wait(Left(x)) → Begin(x)
a(b(c(x))) → c(b(a(x)))
a(c(x)) → a(a(d(a(x))))
d(a(b(x))) → b(a(d(x)))
d(a(c(x))) → b(c(c(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 a d End → Begin a b a d End

Begin a b a d End → Begin a b a d End
by OverlapClosure OC 3
Begin a b a d End → Wait Left a b a d End
by OverlapClosure OC 2
Begin a b → Wait Right4
by original rule (OC 1)
Right4 a d End → Left a b a d End
by OverlapClosure OC 3
Right4 a d End → Aa Left b a d End
by OverlapClosure OC 2
Right4 a → Aa Right4
by original rule (OC 1)
Right4 d End → Left b a d End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO