On equivalence transformations for term rewriting systems

The confluence property is one of the most important properties of term rewriting systems, and various sufficient criteria for proving this property have been widely investigated. A necessary and sufficient criterion for confluence of terminating term ...

We describe conditional rewriting by means of an inference system and capture termination as the absence of infinite inference: that is, all proof attempts must either successfully terminate, or they must fail in finite time. We call this notion ...

This paper presents a counterexample for the open conjecture whether innermost joinability of all critical pairs ensures confluence of innermost terminating term rewriting systems. We then show that innermost joinability of all normalized instances of ...