NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_07_SRS/num-519.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 468 ms)
↳2 NO

(0) Obligation:

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

a(a(a(x))) → b(c(x))
c(b(x)) → a(a(a(a(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 b b b → b c b b b c a c c a a c c a c c c

c b b b → b c b b b c a c c a a c c a c c c
by OverlapClosure OC 3
c b b b → b c b b c b c a a c c a c c c
by OverlapClosure OC 3
c b b b → b c b c b b c a c c c
by OverlapClosure OC 3
c b b b → b c b c b c b c c
by OverlapClosure OC 3
c b b b → b c a a a b c b c c
by OverlapClosure OC 2
c b → b c a c
by OverlapClosure OC 3
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
c b b → a a b c b c c
by OverlapClosure OC 3
c b b → a a a a a b c c
by OverlapClosure OC 2
c b → a a a a c
by original rule (OC 1)
c b → a b c c
by OverlapClosure OC 3
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
c b → b c a c
by OverlapClosure OC 3
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
c b b → b c b c a a c
by OverlapClosure OC 3
c b b → b c a a a a a c
by OverlapClosure OC 2
c b → b c a c
by OverlapClosure OC 3
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)
c b → b c a c
by OverlapClosure OC 3
c b → a a a a c
by original rule (OC 1)
a a a → b c
by original rule (OC 1)

(2) NO