Argument Filterings and Usable Rules for Simply Typed Dependency Pairs
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 first-order dependency pair method and subterm criterion in (Aoto & Yamada, 2005). In this paper, we incorporate termination criteria using reduction pairs and related refinements into the simply typed dependency pair framework using recursive path orderings for S-expression rewriting systems (Toyama, 2008). In particular, we incorporate the usable rules criterion with respect to argument filterings, 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.
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