Expert system for proving termination of rewrite rule programs by path orderings with extended status

We have developed an expert system, called TERMINATOR, which proves the termination of computer programs written as a set of rewrite rules. In TERMINATOR, the knowledge of the proof techniques is represented by a class of partial orderings called path orderings. In particular, the system incorporates the new and powerful orderings called RPOES and KNSES, which are presented in this paper. The two orderings generalize the well-known RPO and KNS orderings with an idea of the extended status proposed in this paper, and can be successfully used to prove the termination of rewrite rules that can not be proved by the conventional knowledge.<>