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-328.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 1899 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO