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 (⇒, 3790 ms)

↳2 NO

(0) Obligation:

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

c(b(x)) → b(a(x))
a(c(x)) → a(b(c(x)))
b(b(x)) → b(c(x))
c(a(x)) → c(c(c(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 (c)^k+1 b c → b (c)^2k+3 b c

b (c)^k+1 b c → b (c)^2k+3 b c
by Equivalent

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

(0) Obligation:

(1) NonTerminationProof (COMPLETE transformation)

(2) NO