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-101.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 318 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO