Argument Filterings and Usable Rules for Simply Typed Dependency Pairs

Abstract. Simply typed term rewriting (Yamada, 2001) is a framework of higher-order term rewriting without bound variables based on Lisp-like syntax. The dependency pair method for the framework has been obtained by extending the rst-order dependency pair method and sub-term criterion in (Aoto & Yamada, 2005). In this paper, we incorporate termination criteria using reduction pairs and related renements into the simply typed dependency pair framework using recursive path order-ings for S-expression rewriting systems (Toyama, 2008). In particular, we incorporate the usable rules criterion with respect to argument lterings, which is a key ingredient to prove the termination in a modular way. The proposed technique has been implemented in a termination prover and an experimental result is reported.