Disproving confluence of term rewriting systems by interpretation and ordering

In order to disprove confluence of term rewriting systems, we develop new criteria for ensuring non-joinability of terms based on interpretation and ordering. We present some instances of the criteria which are amenable for automation, and report on an implementation of a confluence disproving procedure based on these instances. The experiments reveal that our method is successfully applied to automatically disprove confluence of some term rewriting systems, on which state-of-the-art automated confluence provers fail. A key idea to make our method effective is the introduction of usable rules - this allows one to decompose the constraint on rewrite rules into smaller components that depend on starting terms.