2D Dependency Pairs for Proving Operational Termination of CTRSs

Abstract

The notion of *operational termination* captures nonterminating computations due to subsidiary processes that are necessary to issue a *single* `main' step but which often remain `hidden' when the main computation sequence is observed. This highlights *two dimensions* of nontermination: one for the infinite sequencing of computation steps, and the other that concerns the proof of some single steps. For conditional term rewriting systems (CTRSs), we introduce a new *dependency pair framework* which exploits the *bidimensional* nature of conditional rewriting (rewriting steps + satisfaction of the conditions as reachability problems) to obtain a powerful and more expressive framework for proving operational termination of CTRSs.