  By the Thurston stability theorem, a group of C^1 orientation-preserving
diffeomorphisms of the closed unit interval is locally indicable. We show that
the local order structure of orbits gives a stronger criterion for
nonsmoothability that can be used to produce new examples of locally indicable
groups of homeomorphisms of the interval that are not conjugate to groups of
C^1 diffeomorphisms.

Dynamical Systems;Group Theory;Geometric Topology