Interpretation methods constitute a foundation of the termination analysis of term rewriting. From time to time, remarkable instances of interpretation methods appeared, such as polynomial interpretations, matrix interpretations, arctic interpretations, and their variants. In this paper, we introduce a general framework, the tuple interpretation method, that subsumes these variants as well as many previously unknown interpretation methods as instances. Employing the notion of derivers, we prove the soundness of the proposed method in an elegant way. We implement the proposed method in the termination prover NaTT and verify its significance through experiments.

中文翻译：

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终止术语重写的元组解释

解释方法构成了术语改写终止分析的基础。不时出现解释方法的显着实例，例如多项式解释、矩阵解释、北极解释及其变体。在本文中，我们介绍了一个通用框架，即元组解释方法，它将这些变体以及许多以前未知的解释方法作为实例包含在内。使用派生器的概念，我们以一种优雅的方式证明了所提出方法的合理性。我们在终止证明者NaTT中实现了所提出的方法，并通过实验验证了其重要性。