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 (⇒, 2562 ms)

↳2 NO

(0) Obligation:

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

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

a b b (a)^k c b → a b b (a)^2k+4 c b

a b b (a)^k c b → a b b (a)^2k+4 c b
by Equivalent

a b b (a)^k c b → a b b a a (a)^2k+2 c b
by Overlap u with l (ol4)
b (a)^k c b → c (a)^2k+2 c b
by Equivalent
b (a)^k c b → c (a a)^k a a c b
by Overlapping Derivationstructures
b (a)^k c b → (b)^k c a a c b
by Overlap u with r (ol3)
b (a)^k → (b)^k b
by Selfoverlapping OC am2
b a → b b
by original rule (OC 1)
b c b → c a a c b
by OverlapClosure OC 2
b c → c a a
by original rule (OC 1)
a b → a c b
by original rule (OC 1)
(b)^k c → c (a a)^k
by Selfoverlapping OC am1
b c → c a a
by original rule (OC 1)
a b c → a b b a a
by OverlapClosure OC 3
a b c → a c c a a
by OverlapClosure OC 2
a b → a c b
by original rule (OC 1)
b c → c a a
by original rule (OC 1)
c c → b b
by original rule (OC 1)

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO