  The goal of this note is to compare two notions, one coming from the theory
of rewrite systems and the other from proof theory: confluence and cut
elimination. We show that to each rewrite system on terms, we can associate a
logical system: asymmetric deduction modulo this rewrite system and that the
confluence property of the rewrite system is equivalent to the cut elimination
property of the associated logical system. This equivalence, however, does not
extend to rewrite systems directly rewriting atomic propositions.
