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-135.srs

(0) Obligation:

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

a(x) → x
a(b(x)) → x
b(b(x)) → c(x)
c(a(x)) → a(a(b(c(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:
c a a a a ac a a a a a b c b c

c a a a a ac a a a a a b c b c
by OverlapClosure OC 3
c a a a a ac a a a c a b c
by OverlapClosure OC 2
c a ac c
by OverlapClosure OC 3
c a ab b c
by OverlapClosure OC 2
c ab c
by OverlapClosure OC 3
c aa b c
by OverlapClosure OC 3
c aa a b c
by original rule (OC 1)
a
by original rule (OC 1)
a
by original rule (OC 1)
c ab c
by OverlapClosure OC 3
c aa b c
by OverlapClosure OC 3
c aa a b c
by original rule (OC 1)
a
by original rule (OC 1)
a
by original rule (OC 1)
b bc
by original rule (OC 1)
c a a aa a a c a b c
by OverlapClosure OC 3
c a a aa a a a b c a b c
by OverlapClosure OC 3
c a a aa a c a a b c
by OverlapClosure OC 2
c a aa a c c
by OverlapClosure OC 3
c a aa a b b c
by OverlapClosure OC 2
c aa a b c
by original rule (OC 1)
c ab c
by OverlapClosure OC 3
c aa b c
by OverlapClosure OC 3
c aa a b c
by original rule (OC 1)
a
by original rule (OC 1)
a
by original rule (OC 1)
b bc
by original rule (OC 1)
c aa a b c
by original rule (OC 1)
c aa a b c
by original rule (OC 1)
a b
by original rule (OC 1)
c aa a b c
by original rule (OC 1)

(2) NO