We introduce a new framework for elimination-based data flow analysis. We present a simple algorithm and a delayed algorithm that exhibit a worst-case complexity of O(n²){\mathcal O}(n^2) and [(O)\tilde](m)\tilde{{\mathcal O}}(m) . The algorithms use a new compact data structure for representing reducible flow graphs called Annotated Decomposition Trees. This data structure extends a binary tree to represent flowgraph information, dominance relation of flowgraphs, and the topological order of nodes. The construction of the annotated decomposition trees runs in O(n + m){\mathcal O}(n + m) . Experiments were conducted with reducible flowgraphs of the SPEC2000 benchmark suite.