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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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Lexicographic Combination of Reduction Pairs

  • 会议论文

  • 出版模式：

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  • 发表日期：

    2025年

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  • Teppei Saito,
  • Nao Hirokawa

摘要

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.