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-497.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1163 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO