Confluence of Reduction Rules for Lexicographic Ordering Constraints

The lex leader method for breaking symmetry in CSPs typically produces a large set of lexicographic ordering constraints. Several rules have been proposed to reduce such sets whilst preserving logical equivalence. These reduction rules are not generally confluent: they may reach more than one fixpoint, depending on the order of application. These fixpoints vary in size. Smaller sets of lex constraints are desirable so ensuring reduction to a global minimum is essential. We characterise the systems of constraints for which the reduction rules are confluent in terms of a simple feature of the input, and define an algorithm to determine whether a set of lex constraints reduce confluently.