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-3-num-129-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4247 ms)
↳2 NO

(0) Obligation:

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

Begin(b(x)) → Wait(Right1(x))
Begin(b(x)) → Wait(Right2(x))
Begin(c(x)) → Wait(Right3(x))
Right1(a(End(x))) → Left(End(x))
Right2(a(End(x))) → Left(b(c(a(a(End(x))))))
Right3(c(End(x))) → Left(b(End(x)))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right3(a(x)) → Aa(Right3(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right3(b(x)) → Ab(Right3(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Aa(Left(x)) → Left(a(x))
Ab(Left(x)) → Left(b(x))
Ac(Left(x)) → Left(c(x))
Wait(Left(x)) → Begin(x)
a(x) → x
a(b(x)) → x
a(b(x)) → b(c(a(a(x))))
c(c(x)) → 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 b a End → Wait Left b a End

Wait Left b a End → Wait Left b a End
by OverlapClosure OC 3
Wait Left b a End → Wait Left b a a End
by OverlapClosure OC 2
Wait Left → Begin
by original rule (OC 1)
Begin b a End → Wait Left b a a End
by OverlapClosure OC 3
Begin b a End → Wait Left c c a a End
by OverlapClosure OC 3
Begin b a End → Wait Ac Left c a a End
by OverlapClosure OC 3
Begin b a End → Wait Ac Left a b c a a End
by OverlapClosure OC 3
Begin b a End → Wait Ac Aa Left b c a a End
by OverlapClosure OC 2
Begin b a End → Wait Ac Aa Right2 a End
by OverlapClosure OC 3
Begin b a End → Wait Ac Right2 a a End
by OverlapClosure OC 3
Begin b a End → Wait Right2 c a a End
by OverlapClosure OC 3
Begin b a End → Begin b c a a End
by OverlapClosure OC 3
Begin b a End → Wait Left b c a a End
by OverlapClosure OC 2
Begin b → Wait Right2
by original rule (OC 1)
Right2 a End → Left b c a a End
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin b → Wait Right2
by original rule (OC 1)
Right2 c → Ac Right2
by original rule (OC 1)
Right2 a → Aa Right2
by original rule (OC 1)
Right2 a End → Left b c a a End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
a b →
by original rule (OC 1)
Ac Left → Left c
by original rule (OC 1)
c c → b
by original rule (OC 1)
a →
by original rule (OC 1)

(2) NO