  In this paper, we propose a new method for removing all the redundant
inequalities generated by Fourier-Motzkin elimination. This method is based on
an improved version of Balas' work and can also be used to remove all the
redundant inequalities in the input system. Moreover, our method only uses
arithmetic operations on matrices and avoids resorting to linear programming
techniques. Algebraic complexity estimates and experimental results show that
our method outperforms alternative approaches, in particular those based on
linear programming and simplex algorithm.
