Please provide an example of a groupoid

In the paper titled, 'Tannaka–Krein duality for compact groupoids I, Representation theory', the author proves the Peter Weyl theorem on compact groupoids. In the statement, he gives the hypothesis that $\lambda_{u}(G^{v}_{u})\neq 0$, where $\lambda_{u}$ is the right haarsystem with support in $G_{u},u\in G^{0}$.

Here, $G^{v}_{u} = G^{v}\cap G_{u}$ with $G_{u}= d^{-1}(u)$ and $G^{v}= r^{-1}(v)$ , where $d$ and $r$ are domain and range maps respectively from groupoid $G$ to unit space $G^{0}$, defined as $d(x)=x^{-1}x$ and $r(x)=xx^{-1}$.

Can somebody provide an example of a compact groupoid that satisfies this hypothesis?

Here is the Peter Weyl theorem,

In this paper, $X$, is the unit space $G^{0}$.