  We present an exact two-particle solution of the Currie-Hill equations of
Predictive Relativistic Mechanics in $1 + 1$ dimensional Minkowski space. The
instantaneous accelerations are given in terms of elementary functions
depending on the relative particle position and velocities. The general
solution of the equations of motion is given and by studying the global phase
space of this system it is shown that this is a subspace of the full kinematic
phase space.
