Every rational polyhedron has finite split rank: new proof

Abstract

Split rank of a rational polyhedron is finite. The well known proof of this is based on the fact that split closure is stronger than the Chvátal closure, and the Chvátal rank of a rational polyhedron is finite due to the result of Chvátal and Schrijver. In this note we provide an independent proof for the fact that every rational polyhedron has finite split rank. In principal, we construct a nonnegative potential function which decreases by at least one with "every" second split closure unless the integer hull of the polyhedron is reached.