@MISC{Marche94normalisedrewriting, author = {Claude Marche}, title = {Normalised Rewriting and Normalised Completion}, year = {1994} }

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Abstract

We introduce normalised rewriting, a new rewrite relation. It generalises former notions of rewriting modulo E, dropping some conditions on E. For example, E can now be the theory of identity, idempotency, the theory of Abelian groups, the theory of commutative rings. We give a new completion algorithm for normalised rewriting. It contains as an instance the usual AC completion algorithm, but also the wellknown Buchberger's algorithm for computing standard bases of polynomial ideals. We investigate the particular case of completion of ground equations, In this case we prove by a uniform method that completion modulo E terminates, for some interesting E. As a consequence, we obtain the decidability of the word problem for some classes of equational theories. We give implementation results which shows the efficiency of normalised completion with respect to completion modulo AC. 1 Introduction Equational axioms are very common in most sciences, including computer science. Equations can ...