Affiliations: [a] DLSIIS, Universidad Politécnica de Madrid, Spain. r.gutierrez@upm.es
| [b] DSIC & VRAIN, Universitat Politècnica de València, Spain. slucas@dsic.upv.es
| [c] VRAIN, Universitat Politècnica de València, Spain. miguelvitoresv@gmail.com
Correspondence:
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Address for correspondence: Departamento de Sistemas Informáticos y Computación. Universitat Politècnica de València, Camino de Vera s/n, 46022 Valencia, Spain.
Abstract: 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.
