Hydra Battles and AC Termination

Abstract

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-RPO. 2012 ACM Subject Classification Theory of computation → Equational logic and rewriting; Theory of computation → Rewrite systems; Theory of computation → Computability Keywords