Predicative Lexicographic Path Orders: Towards a Maximal Model for Primitive Recursive Functions.

The predicative lexicographic path order (PLPO for short), a syntactic restriction of the lexicographic path order, is presented. As well as lexicographic path orders, several non-trivial primitive recursive equations, e.g., primitive recursion with parameter substitution, unnested multiple recursion, or simple nested recursion, can be oriented with PLPOs. It can be shown that PLPOs however only induce primitive recursive upper bounds for derivation lengths of compatible rewrite systems. This yields an alternative proof of a classical fact that the class of primitive recursive functions is closed under these non-trivial primitive recursive equations. 1998 ACM Subject Classification F.4.1, F.3.3