In the standard framework for worst-case execution time analysis of programs, the main data structure is a single instance integer linear programming that represents the whole program. The instance of this NP-hard problem must be solved to find an estimate for WCET, and it must be refined if the estimate is not tight. We propose a new framework for WCET analysis, based on abstract segment trees (ASTs) as the main data structure. The ASTs have two advantages. First, they allow computing WCET by solving a number of independent small ILP instances. Second, ASTs store more expressive constraints, thus enabling a more efficient and precise refinement procedure. In order to realize our framework algorithmically, we develop an algorithm for WCET estimation on ASTs, and we develop an interpolation-based counterexample-guided refinement scheme for ASTs.