NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z125-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 47 ms)
↳2 NO

(0) Obligation:

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

Begin(f(x)) → Wait(Right1(x))
Begin(a(x)) → Wait(Right2(x))
Begin(c(x)) → Wait(Right3(x))
Begin(s(x)) → Wait(Right4(x))
Begin(f(x)) → Wait(Right5(x))
Right1(c(End(x))) → Left(f(n(a(c(End(x))))))
Right2(n(End(x))) → Left(c(End(x)))
Right3(c(End(x))) → Left(c(End(x)))
Right4(n(End(x))) → Left(f(s(s(End(x)))))
Right5(n(End(x))) → Left(f(n(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))
Right1(n(x)) → An(Right1(x))
Right2(n(x)) → An(Right2(x))
Right3(n(x)) → An(Right3(x))
Right4(n(x)) → An(Right4(x))
Right5(n(x)) → An(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(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(s(x)) → As(Right1(x))
Right2(s(x)) → As(Right2(x))
Right3(s(x)) → As(Right3(x))
Right4(s(x)) → As(Right4(x))
Right5(s(x)) → As(Right5(x))
Af(Left(x)) → Left(f(x))
An(Left(x)) → Left(n(x))
Ac(Left(x)) → Left(c(x))
Aa(Left(x)) → Left(a(x))
As(Left(x)) → Left(s(x))
Wait(Left(x)) → Begin(x)
f(x) → n(c(n(a(x))))
c(f(x)) → f(n(a(c(x))))
n(a(x)) → c(x)
c(c(x)) → c(x)
n(s(x)) → f(s(s(x)))
n(f(x)) → f(n(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 f n End → Wait Left f n End

Wait Left f n End → Wait Left f n End
by OverlapClosure OC 2
Wait Left f → Wait Right5
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin f → Wait Right5
by original rule (OC 1)
Right5 n End → Left f n End
by original rule (OC 1)

(2) NO