A total AC-compatible ordering based on RPO☆

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Abstract

We define a simplification ordering on terms which is AC-compatible and total on non-AC-equivalent ground terms, without any restrictions on the signature like the number of AC-symbols or free symbols.

Unlike previous work by Narendran and Rusinowitch (1991) our AC-RPO ordering is not based on polynomial interpretations, but on a simple extension of the well-known RPO ordering (with a total (arbitrary) precedence on the function symbols). This solves an open question posed e.g. by Bachmair (1992).

A second difference is that this ordering is also defined on terms with variables, which makes it applicable in practice for complete theorem proving strategies with built-in AC-unification and for orienting non-ground rewrite systems.

The ordering is defined in a simple way by means of rewrite rules, and can be easily implemented, since its main component is RPO.

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☆

This paper is is an extended and revised version of [19], where a different formulation of this ordering was given. Here we include a simpler more elegant formulation which moreover works uniformly for both ground terms and terms with variables. We should like to thank Pierre Lescanne for a very useful suggestion in this direction made at RTA-93. This work is partially supported by the Esprit basic research working group 6028, CCL.

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