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-270.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2202 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO