In the standard framework for worst-case execution time (WCET) analysis of programs, the main data structure is a single instance of integer linear programming (ILP) 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

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... puting 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. Furthermore, we extend our framework to obtain parametric estimates of WCET. We experimentally evaluate our approach on a set of examples from WCET benchmark suites and linear-algebra packages. We show that our analysis, with comparable effort, provides WCET estimates that in many cases significantly improve those computed by existing tools.