NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_06/while2-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 28 ms)
↳2 NO

(0) Obligation:

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

Begin(b(x)) → Wait(Right1(x))
Begin(a(x)) → Wait(Right2(x))
Begin(c(x)) → Wait(Right3(x))
Begin(f(x)) → Wait(Right4(x))
Begin(f(x)) → Wait(Right5(x))
Right1(a(End(x))) → Left(d(End(x)))
Right2(b(End(x))) → Left(a(b(End(x))))
Right3(d(End(x))) → Left(f(a(b(b(c(End(x)))))))
Right4(d(End(x))) → Left(f(a(b(End(x)))))
Right5(a(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))
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))
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))
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))
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))
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)) → d(x)
b(a(x)) → a(b(x))
d(c(x)) → f(a(b(b(c(x)))))
d(f(x)) → f(a(b(x)))
a(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:
Wait Left a b End → Wait Left a b End

Wait Left a b End → Wait Left a b End
by OverlapClosure OC 2
Wait Left a → Wait Right2
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a → Wait Right2
by original rule (OC 1)
Right2 b End → Left a b End
by original rule (OC 1)

(2) NO