Termination w.r.t. Q proof of /home/cern_httpd/provide/research/cycsrs/tpdb/TPDB-d9b80194f163/SRS_Standard/Mixed

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

0 QTRS

↳1 NonTerminationProof (⇒, 2203 ms)

↳2 NO

(0) Obligation:

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

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

b a (c)^k b a → b a (c)^2k+1 b a a

b a (c)^k b a → b a (c)^2k+1 b a a
by Overlap u with l (ol4)

a (c)^k b a → b (c)^2k+1 b a a
by Equivalent
a (c)^k b a → b (c c)^k c b a a
by Overlapping Derivationstructures
a (c)^k b a → (a)^k b c b a a
by Overlap u with r (ol3)
a (c)^k → (a)^k a
by Selfoverlapping OC am2
a c → a a
by original rule (OC 1)
a b a → b c b a a
by OverlapClosure OC 2
a b → b c c
by original rule (OC 1)
c a → b a a
by original rule (OC 1)
(a)^k b → b (c c)^k
by Selfoverlapping OC am1
a b → b c c
by original rule (OC 1)

b b → b a
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO