NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z121.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 100 ms)
↳2 NO

(0) Obligation:

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

Begin(f(x)) → Wait(Right1(x))
Begin(f(x)) → Wait(Right2(x))
Begin(b(x)) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Begin(c(x)) → Wait(Right5(x))
Begin(d(x)) → Wait(Right6(x))
Begin(d(d(x))) → Wait(Right7(x))
Begin(d(x)) → Wait(Right8(x))
Right1(f(End(x))) → Left(b(b(b(End(x)))))
Right2(a(End(x))) → Left(f(a(a(End(x)))))
Right3(b(End(x))) → Left(c(c(a(c(End(x))))))
Right4(d(End(x))) → Left(d(a(b(End(x)))))
Right5(c(End(x))) → Left(d(d(d(End(x)))))
Right6(b(End(x))) → Left(d(b(End(x))))
Right7(c(End(x))) → Left(f(End(x)))
Right8(c(d(End(x)))) → Left(f(End(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))
Right7(f(x)) → Af(Right7(x))
Right8(f(x)) → Af(Right8(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))
Right8(b(x)) → Ab(Right8(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))
Right8(a(x)) → Aa(Right8(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))
Right8(c(x)) → Ac(Right8(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))
Right8(d(x)) → Ad(Right8(x))
Af(Left(x)) → Left(f(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Ac(Left(x)) → Left(c(x))
Ad(Left(x)) → Left(d(x))
Wait(Left(x)) → Begin(x)
f(f(x)) → b(b(b(x)))
a(f(x)) → f(a(a(x)))
b(b(x)) → c(c(a(c(x))))
d(b(x)) → d(a(b(x)))
c(c(x)) → d(d(d(x)))
b(d(x)) → d(b(x))
c(d(d(x))) → 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 d b End → Wait Left d b End

Wait Left d b End → Wait Left d b End
by OverlapClosure OC 2
Wait Left d → Wait Right6
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin d → Wait Right6
by original rule (OC 1)
Right6 b End → Left d b End
by original rule (OC 1)

(2) NO