We present an Isabelle/HOL formalization of an earlier result by Suzuki, Middeldorp, and Ida; namely that a certain class of conditional rewrite systems is level-confluent. Our formalization is basically along the lines of the original proof, from which we deviate mostly in the level of detail as well as concerning some basic definitions.
Abstract. We formalize a confluence criterion for the class of quasidecreasing strongly deterministic conditional term rewrite systems in Isabelle/HOL: confluence follows if all conditional critical pairs are joinable. However, quasi-decreasingness, strong determinism, and joinability of conditional critical pairs are all undecidable in general. Therefore, we also formalize sufficient criteria for those properties, which we incorporate into the general purpose certifier CeTA as well as the confluence checker ConCon for conditional term rewrite systems.
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