Sophie, that's similar to the approach I attempted with [#8](https://forum.azimuthproject.org/discussion/comment/18077/#Comment_18077). Does it look right to you? I carry the order on \\(\mathbb{R}^2\\) back to \\(\mathbb{C}\\) by a monoid isomorphism, and observe that monoid automorphisms \\(f : \mathbb{C} \to \mathbb{C}\\) let us produce more partial orders.