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-226-split.srs

(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))
Right1(a(End(x))) → Left(b(c(End(x))))
Right2(c(End(x))) → Left(a(c(b(a(End(x))))))
Right1(a(x)) → Aa(Right1(x))
Right2(a(x)) → Aa(Right2(x))
Right1(b(x)) → Ab(Right1(x))
Right2(b(x)) → Ab(Right2(x))
Right1(c(x)) → Ac(Right1(x))
Right2(c(x)) → Ac(Right2(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)) → b(c(x))
b(x) → x
c(c(x)) → a(c(b(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:
Begin c b c EndBegin c b c End

Begin c b c EndBegin c b c End
by OverlapClosure OC 3
Begin c b c EndWait Left c b c End
by OverlapClosure OC 3
Begin c b c EndWait Ac Left b c End
by OverlapClosure OC 2
Begin c b c EndWait Ac Right1 a End
by OverlapClosure OC 3
Begin c b c EndWait Right1 c a End
by OverlapClosure OC 3
Begin c b c EndBegin b c a End
by OverlapClosure OC 3
Begin c b c EndWait Left b c a End
by OverlapClosure OC 3
Begin c b c EndWait Ab Left c a End
by OverlapClosure OC 2
Begin cWait Right2
by original rule (OC 1)
Right2 b c EndAb Left c a End
by OverlapClosure OC 2
Right2 bAb Right2
by original rule (OC 1)
Right2 c EndLeft c a End
by OverlapClosure OC 3
Right2 c EndLeft c b a End
by OverlapClosure OC 3
Right2 c EndLeft a c b a End
by original rule (OC 1)
a
by original rule (OC 1)
b
by original rule (OC 1)
Ab LeftLeft b
by original rule (OC 1)
Wait LeftBegin
by original rule (OC 1)
Begin bWait Right1
by original rule (OC 1)
Right1 cAc Right1
by original rule (OC 1)
Right1 a EndLeft b c End
by original rule (OC 1)
Ac LeftLeft c
by original rule (OC 1)
Wait LeftBegin
by original rule (OC 1)

(2) NO