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-177.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 138 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO