Use two lists of linear combinations (one in which the resultant terms
include occurrences of the
mth variable with positive coefficients,
and one with negative coefficients) and linearly combine them in every
possible way that eliminates the
First, eliminate all variables by Fourier–Motzkin elimination.
When all variables have been eliminated, find and return the
linear combination which produces a constraint of the form
0 < k + t such that
k is the constant term of the RHS and
k < 0.