Abstract

. We present a concrete example of how one can extract constructive content from a non--constructive proof. The proof investigated is a termination proof of the string--rewriting system 1100 ! 000111. This rewriting system is self--embedding, so the standard termination techniques which rely on Kruskal's Tree Theorem cannot be applied directly. Dershowitz and Hoot [3] have given a classical termination proof using a minimal bad sequence argument. We analyse their proof and give a constructive interpretation of it, which enables us to extract a first proof in Type Theory that uses generalised inductive definitions. By simplifying this constructive proof we obtain a second proof in a theory conservative over primitive recursive arithmetic. This proof is generalised to a theorem about string rewriting systems. 1 Introduction This paper presents a concrete example, from the theory of rewriting systems, illustrating some basic points in proof theory, and providing further motivations for t...

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