Cancellability of committee solution of linear inequalities system

The task of discriminating analysis in easy conditions is reduced to a system of linear inequalities. However, this system may be incompatible, and it is not so rare case. Then, a method of committees. The quality of Committee is improved by reducing the number of its members. Here is the method of reducing the number of members of the Committee, if in principle this is possible. First the particular case of a linear system of inequalities. And the theory of contractility of the Committee. Some examples of committees in space R2 then the theory is generalized to the space Rn. The observation is done concerning the relationship between the minimum and irreducible Committee. The algorithm for finding the minimum of the Committee, based on the fundamental collapse of the system of linear inequalities. However, the question remains of assessing the complexity of the presented algorithm. At the end of the article gives an important sufficient condition is not contractility of the Committee and some Lemma that allows to shorten the algorithm for finding the minimum of the Committee.