Monoids Defined by Rewrite Systems

This is a category of finitely presented monoids where the relations are interpreted as rewrite rules. The most important case is that in which the monoid is defined by a confluent system of rewrite rules. A monoid of this category is typically constructed by applying the Knuth-Bendix procedure to a finitely presented monoid. Magma uses the Knuth-Bendix developed by Derek Holt in his package kbmag.

• Construction of an RWS monoid from an fp-monoid using the Knuth-Bendix procedure. Orderings supported include: RT-recursive, recursive, ShortLex, WT-ShortLex and Wreath
• Test a rewrite system for confluence
• Reduction of a word to normal form
• Operations on words: Product, exponentiation, equality
• Test for a monoid being finite
• Enumeration of elements
• Definition of homomorphisms whose domain or codomain is an RWS monoid