NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_07_size12/size-12-alpha-2-num-19-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2218 ms)
↳2 NO

(0) Obligation:

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

Begin(a(b(x))) → Wait(Right1(x))
Begin(b(x)) → Wait(Right2(x))
Begin(b(b(x))) → Wait(Right3(x))
Begin(b(x)) → Wait(Right4(x))
Right1(a(End(x))) → Left(a(b(b(a(End(x))))))
Right2(a(a(End(x)))) → Left(a(b(b(a(End(x))))))
Right3(b(End(x))) → Left(a(End(x)))
Right4(b(b(End(x)))) → Left(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(x) → x
a(a(b(x))) → a(b(b(a(x))))
b(b(b(x))) → 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:
Wait Left a b b a a End → Wait Left a b b a a End

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

(2) NO