A simple relaxation of two rows of a simplex tableau is a mixed integer set
consisting of two equations with two free integer variables and non-negative
continuous variables. Recently Andersen, Louveaux, Weismantel and Wolsey (2007)
and Cornuejols and Margot (2008) showed that the facet-defining inequalities of
this set are either split cuts or intersection cuts obtained from lattice-free
triangles and quadrilaterals. Through a result by Cook, Kannan and Schrijver
(1990), it is known that one particular class of facet-defining triangle
inequality does not have a finite split rank. In this paper, we show that all
other facet-defining triangle and quadrilateral inequalities have a finite
split-rank. The proof is constructive and given a facet-defining triangle or
quadrilateral inequality we present an explicit sequence of split inequalities
that can be used to generate it.Comment: 39 pages and 13 figure
