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We enhance the dependency pair method in order to prove termination using recursive structure analysis in simply-typed term rewriting systems, which is one of the computational models of functional programs. The primary advantage of our method is that one can exclude higher-order variables which are difficult to analyze theoretically, from recursive(More)
SUMMARY Simply-typed term rewriting systems (STRSs) are an extension of term rewriting systems. STRSs can be naturally handle higher order functions, which are widely used in existing functional programming languages. In this paper we design recursive and lexicographic path orders, which can efficiently prove the termination of STRSs. Moreover we discuss an(More)
Higher-order rewrite systems (HRSs) and simply-typed term rewriting systems (STRSs) are computational models of functional programs. We recently proposed an extremely powerful method, the static dependency pair method, which is based on the notion of strong computability, in order to prove termination in STRSs. In this paper, we extend the method to HRSs.(More)
Automated reasoning of inductive theorems is considered important in program verification. To verify inductive theorems automatically, several implicit induction methods like the inductionless induction and the rewriting induction methods have been proposed. In studying inductive theorems on higher-order rewritings, we found that the class of the theorems(More)
The static dependency pair method is a method for proving the termination of higher-order rewrite systemsà la Nipkow. It combines the dependency pair method introduced for first-order rewrite systems with the notion of strong computability introduced for typed λ-calculi. Argument filterings and usable rules are two important methods of the dependency pair(More)
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(More)
A static dependency pair method, proposed by us, can effectively prove termination of simply-typed term rewriting systems (STRSs). The theoretical basis is given by the notion of strong computability. This method analyzes a static recursive structure based on definition dependency. By solving suitable constraints generated by the analysis result, we can(More)
SUMMARY The completeness (i.e. confluent and terminating) property is an important concept when using a term rewriting system (TRS) as a computational model of functional programming languages. Knuth and Bendix have proposed a procedure known as the KB procedure for generating a complete TRS. A TRS cannot, however, directly handle higher-order functions(More)