action extends to rays by letting $\theta(\pm c(t_1, ..., t_n))=\pm\theta(c(t_1, ..., t_n))$ with $\pm \in \{+, -\}$. It also extends to stars: $\theta\gstar{r_1, ..., r_n} = \gstar{\theta r_1, ..., \theta r_n}$.

We say that two stars $\sigma_1, \sigma_2$ are *$\alpha$-equivalent*, written $\sigma_1 \alphaeq \sigma_2$, when there exists a renaming $\alpha$ such that $\alpha \sigma_1 = \sigma_2$.

In this work, stars will be considered up to $\alpha$-equivalence. We therefore define $\setofstars$ as the set of all stars over a coloured signature $\mathbb{S}$, quotiented by $\alphaeq$.

\[def:constellation\] A constellation $\Sigma$ is a (countable) multiset of stars, i.e. a countable (possibly infinite) set $\abs{\Sigma}$ together with a map $\alpha_\Sigma: \abs{\Sigma}\rightarrow\setofstars$. The variables appearing in $\Sigma$ are considered (sometimes implicitly) bound to their star i.e $\bigcap_{e\in\abs{\Sigma}} \mathtt{vars}(\alpha_\Sigma(e)) = \emptyset$. The set of rays of $\Sigma$ is defined as $\rays{\Sigma}=\{ (s,r) \mid s\in\abs{\Sigma},r\in\abs{\alpha_\Sigma(s)}\}$. A finite constellation will sometimes be written $\Sigma = a_1\sigma_1 + ... + a_n\sigma_n$ ($a_i\in\nat$).

\[ex:constellation\] Here is an example of two finite and an infinite constellation:

-   $\Sigma_{ex} = \gstar{g(x), f(x), +a(f(x))}+\gstar{-a(y), +b(y)}+\gstar{x, -b(g(x))}+\gstar{+b(x), x}$

-   $\Sigma_a = \gstar{-a(x), +a(x), -b(x)}$

-   $\Sigma_\nat$ is defined by $|\Sigma_\nat| = \nat$ and $\alpha_{\Sigma_\nat}(n) = \gstar{-nat.s^n(0), +nat.s^{n+1}(0)}$

where $s^0(t) = t$ and $s^{n+1}(t) = 