NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_05_SRS/aprove3.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 282 ms)
↳2 NO

(0) Obligation:

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

Begin(0(x)) → Wait(Right1(x))
Begin(s(0(x))) → Wait(Right2(x))
Begin(0(x)) → Wait(Right3(x))
Begin(s(s(x))) → Wait(Right4(x))
Begin(s(x)) → Wait(Right5(x))
Begin(s(x)) → Wait(Right6(x))
Begin(i(x)) → Wait(Right7(x))
Begin(s(x)) → Wait(Right8(x))
Right1(p(End(x))) → Left(s(s(0(s(s(p(End(x))))))))
Right2(p(End(x))) → Left(0(End(x)))
Right3(p(s(End(x)))) → Left(0(End(x)))
Right4(p(End(x))) → Left(s(p(s(End(x)))))
Right5(p(s(End(x)))) → Left(s(p(s(End(x)))))
Right6(f(End(x))) → Left(g(q(i(End(x)))))
Right7(q(End(x))) → Left(q(s(End(x))))
Right8(q(End(x))) → Left(s(s(End(x))))
Right1(p(x)) → Ap(Right1(x))
Right2(p(x)) → Ap(Right2(x))
Right3(p(x)) → Ap(Right3(x))
Right4(p(x)) → Ap(Right4(x))
Right5(p(x)) → Ap(Right5(x))
Right6(p(x)) → Ap(Right6(x))
Right7(p(x)) → Ap(Right7(x))
Right8(p(x)) → Ap(Right8(x))
Right1(0(x)) → A0(Right1(x))
Right2(0(x)) → A0(Right2(x))
Right3(0(x)) → A0(Right3(x))
Right4(0(x)) → A0(Right4(x))
Right5(0(x)) → A0(Right5(x))
Right6(0(x)) → A0(Right6(x))
Right7(0(x)) → A0(Right7(x))
Right8(0(x)) → A0(Right8(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))
Right6(s(x)) → As(Right6(x))
Right7(s(x)) → As(Right7(x))
Right8(s(x)) → As(Right8(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(g(x)) → Ag(Right1(x))
Right2(g(x)) → Ag(Right2(x))
Right3(g(x)) → Ag(Right3(x))
Right4(g(x)) → Ag(Right4(x))
Right5(g(x)) → Ag(Right5(x))
Right6(g(x)) → Ag(Right6(x))
Right7(g(x)) → Ag(Right7(x))
Right8(g(x)) → Ag(Right8(x))
Right1(q(x)) → Aq(Right1(x))
Right2(q(x)) → Aq(Right2(x))
Right3(q(x)) → Aq(Right3(x))
Right4(q(x)) → Aq(Right4(x))
Right5(q(x)) → Aq(Right5(x))
Right6(q(x)) → Aq(Right6(x))
Right7(q(x)) → Aq(Right7(x))
Right8(q(x)) → Aq(Right8(x))
Right1(i(x)) → Ai(Right1(x))
Right2(i(x)) → Ai(Right2(x))
Right3(i(x)) → Ai(Right3(x))
Right4(i(x)) → Ai(Right4(x))
Right5(i(x)) → Ai(Right5(x))
Right6(i(x)) → Ai(Right6(x))
Right7(i(x)) → Ai(Right7(x))
Right8(i(x)) → Ai(Right8(x))
Ap(Left(x)) → Left(p(x))
A0(Left(x)) → Left(0(x))
As(Left(x)) → Left(s(x))
Af(Left(x)) → Left(f(x))
Ag(Left(x)) → Left(g(x))
Aq(Left(x)) → Left(q(x))
Ai(Left(x)) → Left(i(x))
Wait(Left(x)) → Begin(x)
p(0(x)) → s(s(0(s(s(p(x))))))
p(s(0(x))) → 0(x)
p(s(s(x))) → s(p(s(x)))
f(s(x)) → g(q(i(x)))
g(x) → f(p(p(x)))
q(i(x)) → q(s(x))
q(s(x)) → s(s(x))
i(x) → s(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 s p s End → Wait Left s p s End

Wait Left s p s End → Wait Left s p s End
by OverlapClosure OC 2
Wait Left s → Wait Right5
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin s → Wait Right5
by original rule (OC 1)
Right5 p s End → Left s p s End
by original rule (OC 1)

(2) NO