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-90.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4404 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO