Termination Proof of S-Expression Rewriting Systems with Recursive Path Relations

Authors:
Yoshihito Toyama
Affiliations:
RIEC, Tohoku University, Aoba-ku, Japan 980-8577
Venue:
RTA '08 Proceedings of the 19th international conference on Rewriting Techniques and Applications
Year:
2008

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Abstract

S-expression rewriting systems were proposed by the author (RTA 2004) for termination analysis of Lisp-like untyped higher-order functional programs. This paper presents a short and direct proof for the fact that every finite S-expression rewriting system is terminating if it is compatible with a recursive path relation with status. By considering well-founded binary relations instead of well-founded orders, we give a much simpler proof than the one depending on Kruskal's tree theorem.