Abstract. This paper provides a new, decidable definition of the higher-order recursive path ordering in which type comparisons are made only when needed, therefore eliminating the need for the computability closure, and bound variables are handled explicitly, making it possible to handle recursors for arbitrary strictly positive inductive types. 1

Termination is a major question in both logic and computer science. In logic, termination is at the heart of proof theory where it is usually called strong normalization (of cut elimination). In computer science, termination has always been an important issue for showing programs correct.

Abstract. In contrast to the current general way of developing tools for proving termination automatically, this paper intends to show an alternative program based on using on the one hand the theory of term orderings to develop powerful and widely applicable methods and on the other hand constraint based techniques to put them in practice. In order to show that this program is realizable a constraint-based framework is presented where ordering based methods for term rewriting, including extensions like Associative-Commutative rewriting, Context-Sensitive rewriting or Higher-Order rewriting, as well as the use of rewriting strategies, can be put in practice in a natural way. 1

Abstract not found

c t i v it y e p o r t 2008 Table of contents

c t i v it y e p o r t

c t i v it y e p o r t 2007 Table of contents

2 Scientific context 175 2.1 Keywords.......................................... 175 2.2 Context and overall goal of the project.......................... 175