Proving termination of programs in ‘real-life’ rewriting-based languages like CafeOBJ , Haskell , Maude , etc., is an important subject of research. To advance this goal, faithfully capturing the impact in the termination behavior of the main language features (e.g., conditions in program rules) is essential. In Part I of this work, we have introduced a 2D Dependency Pair Framework for automatically proving termination properties of Conditional Term Rewriting Systems . Our framework relies on the notion of processor as the main practical device to deal with proofs of termination properties of conditional rewrite systems. Processors are used to decompose and simplify the proofs in a divide and conquer approach. With the basic proof framework defined in Part I, here we introduce new processors to further improve the ability of the 2D Dependency Pair Framework to deal with proofs of termination properties of conditional rewrite systems. We also discuss relevant implementation techniques to use such processors in practice.

中文翻译：

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条件重写系统的 2D 依赖对框架——第二部分：高级处理器和实现技术

证明在“现实生活”中基于重写的语言（如 CafeOBJ、Haskell、Maude 等）中程序的终止是一个重要的研究课题。为了推进这个目标，忠实地捕捉主要语言特性（例如，程序规则中的条件）的终止行为的影响是必不可少的。在这项工作的第一部分，我们介绍了一个 2D 依赖对框架，用于自动证明条件术语重写系统的终止属性。我们的框架依赖于处理器的概念，作为处理条件重写系统终止属性证明的主要实用设备。处理器用于以分而治之的方法分解和简化证明。使用第一部分中定义的基本证明框架，在这里，我们引入了新的处理器，以进一步提高 2D 依赖对框架处理条件重写系统终止属性证明的能力。我们还讨论了在实践中使用此类处理器的相关实现技术。