摘要：Completion is one of the first and most studied techniques in term rewriting and fundamental to automated reasoning with equalities. In an earlier paper we presented a new and formalized correctness proof of abstract completion for finite runs. In this paper we extend our analysis and our formalization to infinite runs, resulting in a new proof that fair infinite runs produce complete presentations of the initial equations. We further consider ordered completion - an important extension of completion that aims to produce ground-complete presentations of the initial equations. Moreover, we revisit and extend results of Métivier concerning canonicity of rewrite systems. All proofs presented in the paper have been formalized in Isabelle/HOL.
