Kira and the block-triangular form

For many state-of-the-art cross section computations the standard approach of Feynman integral reduction with the Laporta algorithm is the main bottleneck of the computation. We study a new approach of Feynman integral reduction by introducing a block-triangular form, which is a smaller system of equations compared to the system of equations which is generated with the Laporta algorithm. The construction of the block-triangular form and its implementation in the program Kira is the main interest of this report.