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-565.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1074 ms)
↳2 NO

(0) Obligation:

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

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

Begin c a End → Begin c a End
by OverlapClosure OC 3
Begin c a End → Wait Left c a End
by OverlapClosure OC 3
Begin c a End → Wait Ac Left a End
by OverlapClosure OC 3
Begin c a End → Wait Ac Aa Left End
by OverlapClosure OC 3
Begin c a End → Wait Ac Aa Left a b End
by OverlapClosure OC 2
Begin c a End → Wait Ac Aa Right3 b End
by OverlapClosure OC 3
Begin c a End → Wait Ac Right3 a b End
by OverlapClosure OC 3
Begin c a End → Wait Ac Right3 b c End
by OverlapClosure OC 3
Begin c a End → Wait Right3 c b c End
by OverlapClosure OC 3
Begin c a End → Begin c c b c End
by OverlapClosure OC 3
Begin c a End → Wait Left c c b c End
by OverlapClosure OC 2
Begin c → Wait Right2
by original rule (OC 1)
Right2 a End → Left c c b c End
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin c → Wait Right3
by original rule (OC 1)
Right3 c → Ac Right3
by original rule (OC 1)
b c → a b
by original rule (OC 1)
Right3 a → Aa Right3
by original rule (OC 1)
Right3 b End → Left a b End
by original rule (OC 1)
a b →
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Ac Left → Left c
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO