We define term rewriting systems on the vertices and faces of nestohedra, and show that the former are confluent and terminating. While the associated posets on vertices generalize Barnard--McConville's flip order for graph-associahedra, the preorders on faces generalize the facial weak order for permutahedra and the generalized Tamari order for associahedra. 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.

翻译：我们在nestohedron的顶点和面上定义了项重写系统，并证明了前者具有合流性与终止性。虽然顶点上的相关偏序集推广了Barnard–McConville为图关联多面体定义的翻转序，但面上的预序则推广了置换多面体的面弱序与关联多面体的广义Tamari序。此外，我们定义并研究了nestohedron的上下文族，其局部合流图满足特定的均匀性条件。其中包括关联多面体与歌剧多面体，其对应重写系统的合流性证明重现了幺半范畴与高阶化operad的范畴相干性定理的证明。