  We extend the techniques of [CH] to build an inductive procedure for studying
actions in the boundary of the Culler-Vogtmann Outer Space, the main novelty
being an adaptation of he classical Rauzy-Veech induction for studying actions
of surface type. As an application, we prove that a tree in the boundary of
Outer space is free and indecomposable if and only if its dual lamination is
minimal up to diagonal leaves. Our main result generalizes [BFH97, Proposition
1.8] as well as the main result of [KL11].
