of DSR [@2+1].

-   On the other hand, in [@rain] a “Correspondence Principle" is formulated in the form that in the low-energy limit of DSR classical GR should be recovered.

A logically different approach to the Lorentz invariance problem is to separate between a particle’s energy and momentum on the one hand and the frequency and wave vector of the associated quantum wave function on the other hand, with the advantage of an immediate connection between the formulations in momentum and in position space and a clear physical meaning of all variables in the game [@SH]. An important consequence is an energy dependent Planck constant, leading to modified uncertainty relations (Generalized Uncertainty Principle, GUP) and possibly, but not necessarily, an energy dependent speed of light.

The above-mentioned correspondence principle and the interpretation of DSR as topological gravity being not equivalent, it is worthwhile to compare low-energy approximations of DSR and GUP to classical gravity in its simplest, i.e. Newtonian form. The program of the present paper is to perform an elementary test, namely to apply these approximations to a scattering process, as possible physical effects always arise in connection with interactions between moving objects. In the current DSR philosophy pseudo-variables 