Recursive Decomposition Ordering and Multiset Orderings

Abstract

The Recursive Decomposition Ordering, a simplification ordering on terms, is useful to prove termination of term rewriting systems. In this paper we give the definition of the decomposition ordering and prove that it is a well-founded simplication ordering containing Dershowitz's Recursive Path Ordering. We also show that the Recursive Decomposition Ordering has a very interesting incremental property. In the second paper, we propose two well-founded orderings on multisets that extend the Dershowitz-Manna ordering. Unlike the Dershowitz-Manna ordering, ours do not have a natural monotonicity property. This lack of monotonicity suggests using monotonicity to provide a new characterization of the Dershowitz -Manna ordering. Section 5 proposes an efficient and correct implementation of that ordering.