The Courcelle's theorem as following:
Obviously, we need the length of the $\varphi$~(that is $||\varphi||$)~in Theorem. However, how to caculate the length of $\varphi$?
For example, $$\begin{aligned} \operatorname{conn}(X)=\quad & \forall_{Y \subseteq V}\left[\left(\exists_{u \in X} u \in Y \wedge \exists_{v \in X} v \notin Y\right)\right.\\ &\left.\Rightarrow\left(\exists_{e \in E} \exists_{u \in X} \exists_{v \in X} \operatorname{inc}(u, e) \wedge \operatorname{inc}(v, e) \wedge u \in Y \wedge v \notin Y\right)\right] . \end{aligned}$$,
$||\operatorname{conn}(X)||=?$, how to caculate it?
