Let $G$ be a finitely generated group. By a theorem of Culler and Morgan, the set of non-abelian (not necessarily simplicial) minimal $\mathbb{R}$-trees with isometric $G$-action injects into the infinite-dimensional vector space $\mathbb{R}^G$ by assigning to each non-abelian tree $T$ its translation length function $l_T\colon G\to\mathbb{R},\ g\mapsto l_T(g)=\inf_{x\in T}d(x,gx)$.

Is there a way to read off of $l_T\in\mathbb{R}^G$ if $T$ is simplicial? For example, if the entries of $l_T$ are bounded below by some positive constant $c>0$, can $T$ still be non-simplicial?

Here, by a *simplicial* tree I mean an $\mathbb{R}$-tree whose set of vertices (i.e. points that when removed disconnect the tree into more than two components) is discrete and closed.

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