Reduced words in certain direct limit of groups

Question

Let $\{ G_i \}_{i \in I}, \{ A_{ij} \}_{i,j \in I}$ be families of groups with injective homomorphisms $A_{ij} \rightarrow G_i$ and $A_{ij} \rightarrow G_j$. Consider the direct limit $$ G:= \varinjlim (G_i, A_{ij}) $$ of this system. I am looking for a structure theorem of reduced words of the elements of $G$. In case $A_{ij} = A$ (a fixed group), this group $G$ is the amalgam of the system at the common group $A$. In this particular case there is a theorem (Theorem 1, Sec1.1, Trees, J. P. Serre). The general version is mentioned (without proof or a statement) in the same reference (Page 5).