To maintain, analyze and reuse many of today's Complex Real-Time Embedded Systems (CRTES) is very difficult and expensive, which, nevertheless, offers high business value in response to great concern in industry. In such context, not only functional behavior but also non-functional properties of systems have to be assured, i.e., Worst-Case Response Time (WCRT) of tasks has to be known. However, due to high complexity of such systems and the nature of the problem, the exact WCRT of tasks is impossible to find in practice, but may only be bounded. In addition, the existing relatively well developed theories for modeling and analysis of real-time systems are having problems which limit their application in the context. In this paper, we address this challenge by presenting a framework for approximate timing analysis of CRTES, namely AESIR-CORES, which provides a tight interval of WCRT estimates of tasks by the usage of two novel contributions. Our evaluation using three models inspired by two fictive but representative industrial CRTES indicates that AESIR-CORES can either successfully obtain the actual WCRT values, or have the potential to bound the unknown actual WCRT values from a statistical perspective.