Normalized completion (Marché 1996) is a widely applicable and efficient technique for completion modulo theories. If successful, a normalized completion procedure computes a rewrite system that allows to decide the validity problem using normalized rewriting. In this paper we consider a slightly simplified inference system for finite normalized completion runs. We prove correctness, show faithfulness of critical pair criteria in our setting, and propose a different notion of normalizing pairs. We then show how normalized completion procedures can benefit from AC-termination tools instead of relying on a fixed AC-compatible reduction order. We outline our implementation of this approach in the completion tool mkbtt and present experimental results, including new completions.
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