NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed_SRS/2-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2945 ms)
↳2 NO

(0) Obligation:

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

Begin(a(a(x))) → Wait(Right1(x))
Begin(a(x)) → Wait(Right2(x))
Begin(a(b(x))) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Right1(a(End(x))) → Left(a(a(b(End(x)))))
Right2(a(a(End(x)))) → Left(a(a(b(End(x)))))
Right3(b(End(x))) → Left(a(b(a(End(x)))))
Right4(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))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right4(b(x)) → Ab(Right4(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Wait(Left(x)) → Begin(x)
a(a(a(x))) → a(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 Aa Left b a a b End
by OverlapClosure OC 3
Begin a b a a b End → Wait Aa Ab Left a a b End
by OverlapClosure OC 2
Begin a b a a b End → Wait Aa Ab Right1 a End
by OverlapClosure OC 3
Begin a b a a b End → Wait Aa Right1 b a End
by OverlapClosure OC 3
Begin a b a a b End → Wait Right1 a 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 Right3
by original rule (OC 1)
Right3 a a b End → Left a a a b a End
by OverlapClosure OC 3
Right3 a a b End → Aa Left a a b a End
by OverlapClosure OC 2
Right3 a → Aa Right3
by original rule (OC 1)
Right3 a b End → Left a a b a End
by OverlapClosure OC 3
Right3 a b End → Aa Left a b a End
by OverlapClosure OC 2
Right3 a → Aa Right3
by original rule (OC 1)
Right3 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 → Wait Right1
by original rule (OC 1)
Right1 a → Aa Right1
by original rule (OC 1)
Right1 b → Ab Right1
by original rule (OC 1)
Right1 a End → Left a a b End
by original rule (OC 1)
Ab Left → Left b
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO