We present a new encoding of the Battle of Hercules and Hydra as a rewrite system with AC symbols. Unlike earlier term rewriting encodings, it faithfully models any strategy of Hercules to beat Hydra. To prove the termination of our encoding, we employ type introduction in connection with many-sorted semantic labeling for AC rewriting and AC-MPO, a new AC compatible reduction order that can be seen as a much weakened version of AC-RPO.

翻译：我们提出了一种将赫拉克勒斯与九头蛇之战编码为包含AC符号的重写系统的新方法。与早期的项重写编码不同，该方法能忠实模拟赫拉克勒斯击败九头蛇的任何策略。为证明该编码的终止性，我们结合AC重写的多类语义标记方法引入类型，并采用AC-MPO——一种可视为AC-RPO极大弱化版本的新型AC相容归约序。