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-127.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 2510 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO