Weighted Path Orders Are Semantic Path Orders

Abstract

We explore the relationship between weighted path orders and (monotonic) semantic path orders. Our findings reveal that weighted path orders can be considered instances of a variant of semantic path orders that comprise order pairs. This observation leads to a generalization of weighted path orders that does not impose simplicity on their underlying algebras. As a result, the generalized version is capable of proving termination of term rewrite systems beyond the realm of simple termination. In order to assess practicality we provide experimental data comparing generalized weighted path orders with the original ones as well as other well-known classes of reduction orders.