NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_07_SRS/num-515.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1238 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO