1 research outputs found
Proving Confluence in the Confluence Framework with CONFident
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