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When rewriting is used to generate convergent and complete rewrite systems in order to answer the validity problem for some theories, all the rewriting theories rely on a same set of notions, properties and methods. Rewriting techniques have mainly been used to answer the validity problem of equational theories, that is to compute congruences. However, recently, they have been extended in order to be applied to other algebraic structures such as pre-orders and orders. In this paper, wedoi:10.1007/s10817-006-9065-7 fatcat:xqjib73s35efdcz3aq2hhgmvle