Recursively Deened Quasi Orders on Terms

We study the problems involved in the recursive de nition of (quasi) orders on terms, focussing on the question of establishing well-de nedness, and the properties required for partial and quasi-orders: irre exivity and transitivity, and re exivity and transitivity, respectively. These properties are in general di cult to establish and this has in many cases come down in the literature as folklore results. Here we present a general scheme that allows us to show that relations are well-de ned and represent partial or quasi-orders. Known path orders as semantic, recursive and lexicographic path order as well as Knuth-Bendix order t into the scheme. Additionally we will also discuss how to obtain other properties commonly found in term orders (amongst which well-foundedness) as an integrated feature of the scheme.