Well-foundedness of term orderings [chapter]

M. C. F. Ferreira, H. Zantema
1995 Lecture Notes in Computer Science  
Well-foundedness is the essential property of orderings for proving termination. We introduce a simple criterion on term orderings such that any term ordering possessing the subterm property and satisfying this criterion is well-founded. The usual path orders fulfil this criterion, yielding a much simpler proof of well-foundedness than the classical proof depending on Kruskal's theorem. Even more, our approach covers non-simplification orders like spo and gpo which can not be dealt with by
more » ... al's theorem. For finite alphabets we present completeness results, i. e., a term rewriting system terminates if and only if it is compatible with an order satisfying the criterion. For infinite alphabets the same completeness results hold for a slightly different criterion.
doi:10.1007/3-540-60381-6_7 fatcat:4v44jhewljazrliphlu3uj2ak4