Abstract
The Knuth–Bendix ordering (KBO) is one of the term orderings in widespread use. We present a new algorithm to compute KBO, which is (to our knowledge) the first asymptotically optimal one. Starting with an ‘obviously correct’ version, we use program transformation to stepwise develop an efficient version, making clear the essential ideas, while retaining correctness. By theoretical analysis we show that the worst-case behavior is thereby changed from quadratic to linear. Measurements show the practical improvements of the different variants.
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Löchner, B. Things to Know when Implementing KBO. J Autom Reasoning 36, 289–310 (2006). https://doi.org/10.1007/s10817-006-9031-4
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DOI: https://doi.org/10.1007/s10817-006-9031-4