NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z119-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 369 ms)
↳2 NO

(0) Obligation:

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

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

Begin f c End → Begin f c End
by OverlapClosure OC 3
Begin f c End → Wait Left f c End
by OverlapClosure OC 2
Begin f → Wait Right4
by original rule (OC 1)
Right4 c End → Left f c End
by OverlapClosure OC 3
Right4 c End → Left d d c End
by original rule (OC 1)
d d → f
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO