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-488.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 475 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO