Proving Confluence in the Confluence Framework with CONFident
This work provides a unified, automated framework for confluence analysis across multiple rewriting formalisms, benefiting researchers in term rewriting and automated reasoning.
The paper introduces the Confluence Framework, a modular divide-and-conquer strategy for proving and disproving confluence in Generalized Term Rewriting Systems, and its implementation in CONFident. The approach automatically handles various rewrite systems including context-sensitive, string, and conditional term rewriting systems.
This article describes the *Confluence Framework*, a novel framework for proving and disproving confluence using a divide-and-conquer modular strategy, and its implementation in CONFident. Using this approach, we are able to automatically prove and disprove confluence of *Generalized Term Rewriting Systems*, where (i) only selected arguments of function symbols can be rewritten and (ii) a rather general class of conditional rules can be used. This includes, as particular cases, several variants of rewrite systems such as (context-sensitive) *term rewriting systems*, *string rewriting systems*, and (context-sensitive) *conditional term rewriting systems*. The divide-and-conquer modular strategy allows us to combine in a proof tree different techniques for proving confluence, including modular decompositions, checking joinability of (conditional) critical and variable pairs, transformations, etc., and auxiliary tasks required by them, e.g., joinability of terms, joinability of conditional pairs, etc.