Consider the Rosenfeld-Groebner algorithm for computing a regular

decomposition of a radical differential ideal generated by a set

of ordinary differential polynomials. This algorithm inputs a

system of differential polynomials and a

ranking on derivatives and constructs finitely many regular systems

equivalent to the original one. The property of

regularity allows to check consistency of the systems and

membership to the corresponding differential ideals.

We propose a bound on the orders of derivatives

occurring in all intermediate and final systems computed by the

Rosenfeld-Groebner algorithm and outline its proof.

We also reduce the problem of conversion of

a regular decomposition of a radical

differential ideal from one ranking to another to a purely

algebraic problem.