Semantic confluence tests and completion methods

We present semantic methods for showing that a term-rewriting system is confluent. We also present methods for completing a given term-rewriting system to obtain an equivalent confluent system. These methods differ from the well-known and widely studied Knuth-Bendix method in that they emphasize semantics rather than syntax. Also, they often require more user interaction than the purely syntactic Knuth-Bendix method. The concept of “ground confluence” is discussed; methods for demonstrating ground confluence are also given. We give decision procedures for some sub-problems that arise in this method.