Dynamic Features of Topographical Multiset Orderings for Terms

Abstract

Multiset orderings are usually used to prove the termination of production systems in comparing elements directly with respect to a given precedence ordering. Topographical multiset orderings are based on the position of elements in the graph induced by the precedence. This concept results in more flexible and stronger multiset orderings. To support. the dynamic aspect of incremental refinement of a multiset ordering the notion of Depth Graphs is introduced. This concept leads to the use of a graph of which the nodes are terms [instead of constants and function symbols]. It replaces the standard precedence graph. Moreover, it can be used to define a new recursive decomposition ordering on terms which is stronger than the original one.