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-373.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 678 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO