On the recursive decomposition ordering with lexicographical status and other related orderings

Abstract

This paper studies three orderings, useful in theorem proving, especially for proving termination of term rewriting systems: the recursive decomposition ordering with status, the recursive path ordering with status and the closure ordering. It proves the transitivity of the recursive path ordering, the strict inclusion of the recursive path ordering in the recursive decomposition ordering, the totality of the recursive path ordering — therefore of the recursive decomposition ordering — the strict inclusion of the recursive decomposition ordering in the closure ordering and the stability of the closure ordering by instantiation.