On Dependency Pair Method for Proving Termination of Higher-Order Rewrite Systems

This paper explores how to extend the dependency pair technique for proving termination of higher-order rewrite systems. In the first order case, the termination of term rewriting systems are proved by showing the non-existence of an infinite R-chain of the dependency pairs. However, the termination and the non-existence of an infinite R-chain do not coincide in the higher-order case. We introduce a new notion of dependency forest that characterize infinite reductions and infinite Rchains, and show that the termination property of higher-order rewrite systems R can be checked by showing the non-existence of an infinite R-chain, if R is strongly linear or non-nested.