The first-order theory of rewriting is decidable for linear variable-separated rewrite systems. We present a new decision procedure which is the basis of FORT, a decision and synthesis tool for properties expressible in the theory. The decision procedure is based on tree automata techniques and verified in Isabelle. Several extensions make the theory more expressive and FORT more versatile. We present a certificate language that enables the output of FORT to be certified by the certifier FORTify generated from the formalization, and we provide extensive experiments.

中文翻译：

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线性变量分离重写系统重写的一阶理论：自动化、形式化、认证

对于线性变量分离重写系统，重写的一阶理论是可判定的。我们提出了一种新的决策程序，它是FORT的基础，这是一种用于在理论中表达的属性的决策和综合工具。决策过程基于树自动机技术并在 Isabelle 中得到验证。一些扩展使该理论更具表现力并使FORT更加通用。我们提出了一种证书语言，使FORT的输出能够由从形式化生成的验证者FORTify进行验证，并且我们提供了广泛的实验。