NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z120-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1390 ms)
↳2 NO

(0) Obligation:

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

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

Begin c c a c End → Begin c c a c End
by OverlapClosure OC 3
Begin c c a c End → Begin d b a c End
by OverlapClosure OC 3
Begin c c a c End → Begin d d End
by OverlapClosure OC 3
Begin c c a c End → Wait Left d d End
by OverlapClosure OC 2
Begin c c a → Wait Right1
by original rule (OC 1)
Right1 c End → Left d d End
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
d → b a c
by OverlapClosure OC 2
d → b c
by original rule (OC 1)
b c → b a c
by original rule (OC 1)
d b → c c
by original rule (OC 1)

(2) NO