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-556.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3464 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(b(b(c(a(a(End(x))))))))
Right3(b(End(x))) → Left(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(b(b(c(a(a(x))))))
b(c(x)) → 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 c c a a End → Wait Left c c a a End

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

(2) NO