  It is pointed out that separability problem for arbitrary multi-partite
states can be fully solved by a finite size, elementary recursive algorithm. In
the worse case scenario, the underlying numerical procedure, may grow doubly
exponentially with the state's rank. Nevertheless, we argue that for generic
states, analysis of concurrence matrices essentially reduces the task of
solving separability problem in $m \times n$ dimensions to solving a set of
linear equations in about $\binom{mn+D-1}{D}$ variables, where $D$ decreases
with $mn$ and for large $mn$ it should not exceed 4. Moreover, the same method
is also applicable to multipartite states where it is at least equally
efficient.
