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                <term xml:lang="en">term rewriting</term>
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              <p>We investigate the unification problemin theories defined by rewrite systems which are both convergent andforward-closed. These theories are also known in the context ofprotocol analysis as theories with the finite variant property andadmit a variant-based unification algorithm.  In this paper, wepresent a new rule-based unification algorithm which can be seen as analternative to the variant-based approach.  In addition, we defineforward-closed combination to capture the union of a forward-closedconvergent rewrite system with another theory, such as theAssociativity-Commutativity, whose function symbols may occur inright-hand sides of the rewrite system. Finally, we present acombination algorithm for this particular class of non-disjoint unionsof theories.</p>
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              <p>On étudie le problème d’unification dans les théories définies par des systèmes deréécriture qui sont à la fois convergents et fermés en avant. Ces théories sont connues dans lecontexte de l’analyse de protocoles de sécurité comme les théories ayant la propriété des variantsfinis et admettant de ce fait un algorithme d’unification à base de variants. Dans ce papier,on présente un nouvel algorithme d’unification à base de règles qui peut être vu comme unealternative à l’approche basée sur le calcul de variants. On étudie l’union d’un système deréécriture convergent et fermé en avant avec une autre théorie dont les symboles de fonctionpeuvent apparaître dans les membres droits du système de réécriture. Finalement, on présenteun algorithme de combinaison pour cette classe particulière d’unions non-disjointes de théories.</p>
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