NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Bouchare_06/09.srs

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

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

(0) Obligation:

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

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

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

(2) NO