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arXiv · 2608.19683

Lexicographic Combination of Reduction Pairs (Extended Version)

Teppei Saito·Nao Hirokawa
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Abstract

We present a simple criterion for combining reduction pairs lexicographically. The criterion is applicable to arbitrary classes of reduction pairs, such as the polynomial interpretation, the matrix interpretation, and the Knuth-Bendix order. In addition, we investigate a variant of the matrix interpretation where the lexicographic order is employed instead of the usual component-wise order. Effectiveness is demonstrated by experiments and examples, including Touzet's Hydra Battle.

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Teppei Saito, Nao Hirokawa. 2026-08-20. Lexicographic Combination of Reduction Pairs (Extended Version). https://arxiv.org/abs/2608.19683

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