connected components to a single vertex.

In Girard’s first paper on Transcendental Syntax [@girard2017transcendental], the constellation $\Sigma = \gstar{+a.x, -a.x, +b.x}$ is mentioned as a counter-example for the Church-Rosser property. Here, we have $\exec^{\mathrm{tree}}_{\{a\}}(\exec^{\mathrm{tree}}_{\{b\}}(\Sigma)) = \exec^{\mathrm{tree}}_{\{b\}}(\exec^{\mathrm{tree}}_{\{a\}}(\Sigma)) = \emptyset$ (because no saturated diagram on $a$ nor on $b$ can be constructed). Our understanding of Girard’s failure comes from his limitation to strongly normalising constellations, so that $\exec^{\mathrm{tree}}_{\{a\}}(\Sigma)$ was not defined.

Remarkable examples of constellations {#subsec:examples}
-------------------------------------

We now explain how the stellar resolution model generalises several established frameworks from the literature.

### (Hyper)graphs

As a first example, we detail how graphs (and more generally hypergraphs) can be encoded, and how the execution coincides with the computation of paths. A consequence of this result is that models of computation such as *Interaction Graphs* [@seiller2012interaction; @seiller2016interaction] are special cases of our construction.

\[ex:graphencoding\] Let $G=(V,E,s,t)$ be a directed hypergraph, i.e. $s,t$ are maps $E\rightarrow\wp(V)$. We suppose given a signature in which there exists distinct unary function symbols to represent the elements of $V$ and $E$. Then, for each $e\in E$ with $s(e)=\{v_1,\dots, v_n\}$ and $t(e)=\{w_1,\dots,w_m\}$, we define the star $$\bar{e}=\gstar{-v_1(x), -v_2(x),\dots -v_n(x), +w_1(e(x)), +w_2(e(x)),\dots, +w_m(e(x))}.$$ The graph $G$ is then represented by the 