NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_05_SRS/aprove2.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 50 ms)
↳2 NO

(0) Obligation:

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

Begin(h(x)) → Wait(Right1(x))
Begin(s(s(s(x)))) → Wait(Right2(x))
Begin(s(s(x))) → Wait(Right3(x))
Begin(s(x)) → Wait(Right4(x))
Begin(h(x)) → Wait(Right5(x))
Begin(f(s(s(x)))) → Wait(Right6(x))
Begin(s(s(x))) → Wait(Right7(x))
Begin(s(x)) → Wait(Right8(x))
Begin(a(x)) → Wait(Right9(x))
Right1(g(End(x))) → Left(g(f(s(End(x)))))
Right2(f(End(x))) → Left(h(f(s(h(End(x))))))
Right3(f(s(End(x)))) → Left(h(f(s(h(End(x))))))
Right4(f(s(s(End(x))))) → Left(h(f(s(h(End(x))))))
Right5(f(End(x))) → Left(h(f(s(h(End(x))))))
Right6(f(End(x))) → Left(s(s(s(f(f(End(x)))))))
Right7(f(f(End(x)))) → Left(s(s(s(f(f(End(x)))))))
Right8(f(f(s(End(x))))) → Left(s(s(s(f(f(End(x)))))))
Right9(b(End(x))) → Left(a(b(End(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))
Right9(g(x)) → Ag(Right9(x))
Right1(h(x)) → Ah(Right1(x))
Right2(h(x)) → Ah(Right2(x))
Right3(h(x)) → Ah(Right3(x))
Right4(h(x)) → Ah(Right4(x))
Right5(h(x)) → Ah(Right5(x))
Right6(h(x)) → Ah(Right6(x))
Right7(h(x)) → Ah(Right7(x))
Right8(h(x)) → Ah(Right8(x))
Right9(h(x)) → Ah(Right9(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))
Right9(f(x)) → Af(Right9(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))
Right9(s(x)) → As(Right9(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))
Right9(b(x)) → Ab(Right9(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))
Right9(a(x)) → Aa(Right9(x))
Ag(Left(x)) → Left(g(x))
Ah(Left(x)) → Left(h(x))
Af(Left(x)) → Left(f(x))
As(Left(x)) → Left(s(x))
Ab(Left(x)) → Left(b(x))
Aa(Left(x)) → Left(a(x))
Wait(Left(x)) → Begin(x)
g(h(x)) → g(f(s(x)))
f(s(s(s(x)))) → h(f(s(h(x))))
f(h(x)) → h(f(s(h(x))))
h(x) → x
f(f(s(s(x)))) → s(s(s(f(f(x)))))
b(a(x)) → a(b(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 Right9
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin a → Wait Right9
by original rule (OC 1)
Right9 b End → Left a b End
by original rule (OC 1)

(2) NO