Abstract
We give a fast method for generating reduced sets of rewrite rules equivalent to a given set of ground equations. Since, as we show, reduced ground rewrite systems are in fact canonical, this is essentially an efficient Knuth-Bendix procedure for the ground case. The method runs in O(n log n), where n is the number of occurrences of symbols in E. We also show how our method provides a precise characterization of the (finite) collection of all reduced sets of rewrite rules equivalent to a given ground set of equations E, and prove that our algorithm is complete in that it can enumerate every member of this collection. Finally, we show how to modify the method so that it takes as input E and a total precedence ordering on the symbols in E, and returns a reduced rewrite system contained in the lexicographic path ordering generated by the precedence.
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© 1989 Springer-Verlag Berlin Heidelberg
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Snyder, W. (1989). Efficient ground completion. In: Dershowitz, N. (eds) Rewriting Techniques and Applications. RTA 1989. Lecture Notes in Computer Science, vol 355. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-51081-8_123
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DOI: https://doi.org/10.1007/3-540-51081-8_123
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