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-564.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4567 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO