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-233.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1878 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO