A term rewrite system is terminating when no infinite reduction sequences are possible. Relative termination generalizes termination by permitting infinite reductions as long as some distinguished rules are not applied infinitely many times. Relative termination is thus a fundamental notion that has been used in a number of different contexts, like analyzing the confluence of rewrite systems or the termination of narrowing. In this work, we introduce a novel technique to prove relative termination by reducing it to dependency pair problems. To the best of our knowledge, this is the first significant contribution to Problem #106 of the RTA List of Open Problems. We first present a general approach that is then instantiated to provide a concrete technique for proving relative termination. The practical significance of our method is illustrated by means of an experimental evaluation.

中文翻译：

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通过依赖对的相对终止

当不可能有无限减少序列时，术语重写系统将终止。相对终止通过允许无限归约来概括终止，只要某些显着规则不是无限​​次应用即可。因此，相对终止是一个基本概念，已在许多不同的上下文中使用，例如分析重写系统的汇合或缩小的终止。在这项工作中，我们引入了一种新技术来通过将其简化为依赖对问题来证明相对终止。据我们所知，这是对 RTA 未决问题列表问题 #106 的第一个重要贡献。我们首先提出一种通用方法，然后实例化该方法以提供用于证明相对终止的具体技术。