NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Zantema_04/z128.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:

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

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

(2) NO