Iterative Path Orders Extended abstract

In the first half of this paper we give an alternative version of the recursive path order (RPO) for first-order term rewriting, which is ‘iterative’ rather than recursive. Hence the name iterative path order (IPO).In the second part of the paper we prove that IPO is a well-founded order, by a simple argument familiar from Proof Theory. To this end we employ a labeled extension of IPO.The result is an easy to grasp and powerful termination proof technique, whose correctness proof avoids the usual appeal to Kruskal’s Tree Theorem.We finally argue that the method is extendible to the lexicographic case and tothe higher-order case.The IPO method is easily seen to be as powerful as the usual RPO. In fact, the orderings are equivalent. This result requires a fine-grained analysis of IPO, that is added in an Appendix. _____________