Philip Zucker • 12/22/2025

An Inequality Union Find Inspired by Atomic Asymmetric Completion

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The article details asymmetric completion, a technique adapting Knuth-Bendix completion to handle inequality relations (like subsets) using dual rewrite systems (R and S). It explains the theoretical basis, contrasts it with equational reasoning, and discusses implementation strategies, including a basic Python prototype using sets and potential optimizations with heaps and sorted merges.

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#Union Find #Egraph #Rewrite Systems
An Inequality Union Find Inspired by Atomic Asymmetric Completion

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