An ordinal calculus for proving termination in term rewriting
In this article, we are concerned with the proofs of termination of rewrite systems by the method of interpretations. We propose a modified approach to subrecursive hierarchies of functions by means of a syntactical approach to ordinal recursion. Our method appears to be appropriate for finding interpretations in a systematic way. We provide several examples of applications. It is shown that three usual recursion schemas over the natural numbers, recursion with parameter substitution, simple nested recursion and unnested multiple recursion can be encoded directly in our system. As the corresponding ordinal terms are primitive recursively closed, we get a concise and intuitive proof for the closure of the class of primitive recursive functions under these schemes.
Keywordsrewrite systems termination primitive recursion ordinal recursion
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