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Evaluating the reliability of Internet routing is important for an ISP to assess existing peer relationships or establish new peer relationships. Existing algorithms for network reliability computations take all routing paths as inputs. However, these paths may not be actually available for routing because of the constraints of routing policies in the Internet. In this paper, we propose an algebraic approach that effectively reduces the number of candidate routing paths according to the given routing policy. We further improve the accuracy of the routing reliability result by subtracting the miscounted value of routing paths due to overlooking routing policy constraints.