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-474.srs

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

0 QTRS
↳1 NonTerminationProof (⇒, 4843 ms)
↳2 NO

(0) Obligation:

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

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

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

(2) NO