Term rewriting on nestohedra

We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated poset on vertices generalizes Barnard--McConville's flip order for graph-associahedra, the preorder on faces likely generalizes the facial weak order for permutahedra. Moreover, we define and study contextual families of nestohedra, whose local confluence diagrams satisfy a certain uniformity condition. Among them are associahedra and operahedra, whose associated proofs of confluence for their rewriting systems reproduce proofs of categorical coherence theorems for monoidal categories and categorified operads.