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Bounds and algebraic algorithms in differential algebra: the ordinary case Moreno Maza, Marc Golubitsky, Oleg Kondratieva, Marina V. Ovchinnikov, Alexey Differential algebra Rosenfeld Groebner Algorithm 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Marc Moreno Maza and Oleg Golubitsky and Marina V. Kondratieva and Alexey Ovchinnikov 2007 Is Part Of Dagstuhl Seminar Proceedings, Volume 6271, Challenges in Symbolic Computation Software (2006) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/DagSemProc.06271.4 urn:nbn:de:0030-drops-10219 https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.06271.4 eng https://creativecommons.org/licenses/by/4.0/legalcode