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

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

0 QTRS
↳1 NonTerminationProof (⇒, 670 ms)
↳2 NO

(0) Obligation:

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

Begin(c(x)) → Wait(Right1(x))
Begin(f(c(x))) → Wait(Right2(x))
Begin(c(x)) → Wait(Right3(x))
Begin(g(x)) → Wait(Right4(x))
Begin(f(g(x))) → Wait(Right5(x))
Begin(g(x)) → Wait(Right6(x))
Right1(g(End(x))) → Left(g(f(c(End(x)))))
Right2(g(End(x))) → Left(g(f(f(c(End(x))))))
Right3(g(f(End(x)))) → Left(g(f(f(c(End(x))))))
Right4(g(End(x))) → Left(g(f(g(End(x)))))
Right5(f(End(x))) → Left(g(f(End(x))))
Right6(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))
Right4(g(x)) → Ag(Right4(x))
Right5(g(x)) → Ag(Right5(x))
Right6(g(x)) → Ag(Right6(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))
Right1(f(x)) → Af(Right1(x))
Right2(f(x)) → Af(Right2(x))
Right3(f(x)) → Af(Right3(x))
Right4(f(x)) → Af(Right4(x))
Right5(f(x)) → Af(Right5(x))
Right6(f(x)) → Af(Right6(x))
Ag(Left(x)) → Left(g(x))
Ac(Left(x)) → Left(c(x))
Af(Left(x)) → Left(f(x))
Wait(Left(x)) → Begin(x)
g(c(x)) → g(f(c(x)))
g(f(c(x))) → g(f(f(c(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 Right4
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin g → Wait Right4
by original rule (OC 1)
Right4 f f g End → Left g f f g End
by OverlapClosure OC 3
Right4 f f g End → Left f f g f g End
by OverlapClosure OC 3
Right4 f f g End → Af Left f g f g End
by OverlapClosure OC 2
Right4 f → Af Right4
by original rule (OC 1)
Right4 f g End → Left f g f g End
by OverlapClosure OC 3
Right4 f g End → Af Left g f g End
by OverlapClosure OC 2
Right4 f → Af Right4
by original rule (OC 1)
Right4 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