  In a previous article, analytic 1-submanifolds had been classified w.r.t.
their symmetry under a given regular and separately analytic Lie group action
on an analytic manifold. It was shown that such an analytic 1-submanifold is
either free or (via the exponential map) analytically diffeomorphic to the unit
circle or an interval. In this paper, we show that each free analytic
1-submanifold is discretely generated by the symmetry group, i.e., naturally
decomposes into countably many symmetry free segments that are mutually and
uniquely related by the Lie group action. This is proven under the assumption
that the action is non-contractive (which is less restrictive than regular and
separately analytic).
