Knuth-Bendix Algorithm

The Knuth-Bendix algorithm[Knuth, D. E and Bendix, P. E., ``Simple word problems in universal algebras'', in J. Leech (ed.), Computational Problems in Abstract Algebra, Pergammon Press, 1970, pp. 263-297.] describes how to derive a complete set of rewrite rules R from an equational theory E , such that:

If E implies that two terms s and t are equal, then the reductions in R will rewrite both s and t to the same irreducible form in a finite number of steps.

Two properties are needed:

The Knuth-Bendix algorithm is based on a well-founded ordering of terms so that each rewriting step makes the result ``smaller''.

Unfortunately, rather simple systems do not have a Knuth-Bendix solution.

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