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-450.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 601 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO