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-532.srs-torpacyc2out-split.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3994 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(c(x)) → Wait(Right3(x))
Begin(c(x)) → Wait(Right4(x))
Right1(a(End(x))) → Left(c(End(x)))
Right2(a(a(End(x)))) → Left(c(End(x)))
Right3(a(End(x))) → Left(b(c(a(a(End(x))))))
Right4(b(End(x))) → Left(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))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(x))
Right3(c(x)) → Ac(Right3(x))
Right4(c(x)) → Ac(Right4(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(a(b(x))) → c(x)
a(c(x)) → 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:
Begin c a a End → Begin c a a End

Begin c a a End → Begin c a a End
by OverlapClosure OC 3
Begin c a a End → Wait Left c a a End
by OverlapClosure OC 3
Begin c a a End → Wait Ac Left a a End
by OverlapClosure OC 3
Begin c a a End → Wait Ac Left a c End
by OverlapClosure OC 3
Begin c a a End → Wait Ac Aa Left c End
by OverlapClosure OC 2
Begin c a a End → Wait Ac Aa Right1 a End
by OverlapClosure OC 3
Begin c a a End → Wait Ac Right1 a a End
by OverlapClosure OC 3
Begin c a a End → Wait Right1 c a a End
by OverlapClosure OC 3
Begin c a a End → Begin a b c a a End
by OverlapClosure OC 3
Begin c a a End → Wait Left a b c a a End
by OverlapClosure OC 2
Begin c → Wait Right3
by original rule (OC 1)
Right3 a a End → Left a b c a a End
by OverlapClosure OC 3
Right3 a a End → Aa Left b c a a End
by OverlapClosure OC 2
Right3 a → Aa Right3
by original rule (OC 1)
Right3 a End → Left b c a a End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)
Begin a b → Wait Right1
by original rule (OC 1)
Right1 c → Ac Right1
by original rule (OC 1)
Right1 a → Aa Right1
by original rule (OC 1)
Right1 a End → Left c End
by original rule (OC 1)
Aa Left → Left a
by original rule (OC 1)
a c → a a
by OverlapClosure OC 3
a c → b c a a
by original rule (OC 1)
b c →
by original rule (OC 1)
Ac Left → Left c
by original rule (OC 1)
Wait Left → Begin
by original rule (OC 1)

(2) NO