  This article presents a validation of a recently proposed strongly
polynomial-time algorithm for the general linear programming problem. The
algorithm is an implicit, solution-space reduction procedure that works as
follows. Primal and dual problems are combined into a special system of linear
equations constrained by complementarity relations and non-negative variables.
Each iteration of the algorithm consists of applying two complementary
Gauss-Jordan pivoting operations, guided by a reduction lemma. The algorithm
requires no more than m+n iterations, where m is the number of constraints and
n is the number of variables of the general linear programming problem. In
another arXiv article, arXiv:2309.01037[math.DC], a numerical illustration of
the algorithm is given that includes an instance of a classical problem of Klee
and Minty and a problem of Beale.
