NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/01.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2059 ms)
↳2 NO

(0) Obligation:

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

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

Begin a b a a b End → Begin a b a a b End
by OverlapClosure OC 3
Begin a b a a b End → Wait Left a b a a b End
by OverlapClosure OC 3
Begin a b a a b End → Wait Left b a b a b End
by OverlapClosure OC 3
Begin a b a a b End → Wait Ab Left a b a b End
by OverlapClosure OC 2
Begin a b a a b End → Wait Ab Right1 a End
by OverlapClosure OC 3
Begin a b a a b End → Wait Right1 b a End
by OverlapClosure OC 3
Begin a b a a b End → Begin a a a b a End
by OverlapClosure OC 3
Begin a b a a b End → Wait Left a a a b a End
by OverlapClosure OC 2
Begin a b → Wait Right4
by original rule (OC 1)
Right4 a a b End → Left a a a b a End
by OverlapClosure OC 3
Right4 a a b End → Aa Left a a b a End
by OverlapClosure OC 2
Right4 a → Aa Right4
by original rule (OC 1)
Right4 a b End → Left a a b a End
by OverlapClosure OC 3
Right4 a b End → Aa Left a b a End
by OverlapClosure OC 2
Right4 a → Aa Right4
by original rule (OC 1)
Right4 b End → Left a b a End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin a a a → Wait Right1
by original rule (OC 1)
Right1 b → Ab Right1
by original rule (OC 1)
Right1 a End → Left a b a b End
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
b a b → a b a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO