Higher-Order Constrained Dependency Pairs for (Universal) Computability

Abstract

Dependency pairs constitute a series of very effective techniques for the termination analysis of term rewriting systems. In this paper, we adapt the static dependency pair framework to logically constrained simply-typed term rewriting systems (LCSTRSs), a higher-order formalism with logical constraints built in. We also propose the concept of universal computability, which enables a form of open-world termination analysis through the use of static dependency pairs.