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-170.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1850 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO