  We investigated the distinction between two kinds of "Complexity equals
Action"(CA) conjecture counting methods which are separately provided by Brown
$ et\, al. $ and Lehner $et\, al.$ separately. For the late-time CA complexity
growth rate, we show that the difference between two counting methods only
comes from the boundary term of the segments on the horizon. However, both
counting methods give the identical late-time result. Our proof is general,
independent of the underlying theories of higher curvature gravity as well as
the explicit stationary spacetime background. To be specific, we calculate the
late-time action growth rate in SAdS black hole for F(Ricci) gravity, and show
that these two methods actually give the same result. Moreover, by using the
Iyer-Wald formalism, we find that the full action rate within the WDW patch can
be expressed as some boundary integrations, and the final contribution only
comes from the boundary on singularity. Although the definitions of the mass of
black hole has been modified in F(Ricci) gravity, its late-time result has the
same form with that of SAdS black hole in Einstein gravity.
