DescriptionThe Rips machine is a method of studying the action of groups on real trees. Roughly speaking, the Rips machine is an algorithm that takes as input a finite 2-complex equipped with a transversely measured lamination, namely a band complex, and puts it in a “normal form”, which is the disjoint union of finitely many sub-laminations. Each component of this normal form belongs to one of the four types: simplicial, surface, toral and thin. The earlier three types are well- studied, whereas thin type does not have a standard model. The first part of this thesis provides an additional structure for thin type components of band complexes. The second part of this paper develops a version of the Rips machine which studies pairs of band complexes. The goal of this machine is to convert pairs of band complexes into standard forms which can be further used to study sub- laminations and subgroup actions.