NO Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Waldmann_07_size11/size-11-alpha-3-num-1.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4240 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO