A left-order on a group G is totally determined by its positive cone P, that is the elements in G that are greater than the identity. The set P is a subsemigroup and we can ask ourselves when this semigroup can be finitely generated, described by a regular language, etc. A recent result of S.Hermiller and Z.Sunic shows that non-abelian free groups do not have regular positive cones. I will discuss this and how to generalize this result to limit groups. The talk will be based on joint work with C.Rivas and I will report some results of my PhD student H.L.Su. (Yago Antolin is from the Unversidad Autónoma de Madrid)