Abstract
Like Narendran and Rusinowitch [NR91], we define a simplification ordering 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.
An important difference w.r.t. their work is that our ordering is not based on polynomial interpretations, but on a total (arbitrary) precedence on the function symbols, like in LPO or RPO (this solves an open question posed e.g. by Bachmair [Bac91]).
A second difference is that we define an extension to terms with variables, which makes the ordering applicable in practice for complete theorem proving strategies with built-in AC-unification and for orienting non-ground rewrite systems.
Our ordering is defined in a simple way by means of rewrite rules, and can be easily (and efficiently) implemented, since its main component is RPO.
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Rubio, A., Nieuwenhuis, R. (1993). A precedence-based total AC-compatible ordering. In: Kirchner, C. (eds) Rewriting Techniques and Applications. RTA 1993. Lecture Notes in Computer Science, vol 690. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-21551-7_28
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DOI: https://doi.org/10.1007/978-3-662-21551-7_28
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