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-47.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 773 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO