NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Secret_07_SRS/num-525.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 3575 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO