NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z013.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 140 ms)
↳2 NO

(0) Obligation:

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

Begin(g(x)) → Wait(Right1(x))
Begin(f(g(x))) → Wait(Right2(x))
Begin(g(x)) → Wait(Right3(x))
Right1(g(End(x))) → Left(g(f(g(End(x)))))
Right2(f(End(x))) → Left(g(f(End(x))))
Right3(f(f(End(x)))) → Left(g(f(End(x))))
Right1(g(x)) → Ag(Right1(x))
Right2(g(x)) → Ag(Right2(x))
Right3(g(x)) → Ag(Right3(x))
Right1(f(x)) → Af(Right1(x))
Right2(f(x)) → Af(Right2(x))
Right3(f(x)) → Af(Right3(x))
Ag(Left(x)) → Left(g(x))
Af(Left(x)) → Left(f(x))
Wait(Left(x)) → Begin(x)
g(g(x)) → g(f(g(x)))
f(f(g(x))) → g(f(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 g f f g End → Wait Left g f f g End

Wait Left g f f g End → Wait Left g f f g End
by OverlapClosure OC 2
Wait Left g → Wait Right1
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin g → Wait Right1
by original rule (OC 1)
Right1 f f g End → Left g f f g End
by OverlapClosure OC 3
Right1 f f g End → Left f f g f g End
by OverlapClosure OC 3
Right1 f f g End → Af Left f g f g End
by OverlapClosure OC 2
Right1 f → Af Right1
by original rule (OC 1)
Right1 f g End → Left f g f g End
by OverlapClosure OC 3
Right1 f g End → Af Left g f g End
by OverlapClosure OC 2
Right1 f → Af Right1
by original rule (OC 1)
Right1 g End → Left g f g End
by original rule (OC 1)
Af Left → Left f
by original rule (OC 1)
Af Left → Left f
by original rule (OC 1)
f f g → g f
by original rule (OC 1)

(2) NO