Aart Middeldorp

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Developing automatable methods for proving termination of term rewrite systems that resist traditional techniques based on simplification orders has become an active research area in the past few years. The dependency pair method of Arts and Giesl is one of the most popular such methods. However, there are several obstacles that hamper its automation. In(More)
In this paper we analyze completeness results for basic narrowing. We show that basic narrowing is not complete with respect to normalizable solutions for equational theories defined by confluent term rewriting systems, contrary to what has been conjectured. By imposing syntactic restrictions on the rewrite rules we recover completeness. We refute a result(More)
This paper describes the Tyrolean Termination Tool (TTT in the sequel), the successor of the Tsukuba Termination Tool [12]. We describe the differences between the two and explain the new features, some of which are not (yet) available in any other termination tool, in some detail. TTT is a tool for automatically proving termination of rewrite systems based(More)
A term rewriting system is called complete if it is both confluent and strongly normalising. Barendregt and Klop showed that the disjoint union of complete term rewriting systems does not need to be complete. In other words, completeness is not a modular property of term rewriting systems. Toyama, Klop and Barendregt showed that completeness is a modular(More)
In this paper we present some new refinements of the dependency pair method for automatically proving the termination of term rewrite systems. These refinements are very easy to implement, increase the power of the method, result in simpler termination proofs, and make the method more efficient.