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Symbolic terminal reliability algorithms are important for analysis and synthesis of computer networks. In this paper, we present a simple and efficient algorithm, SYREL, to obtain compact terminal reliability expressions between a terminal pair of computers of complex networks. This algorithm incorporates conditional probability,, set theory, and Boolean algebra in a distinct approach in which most of the computations performed are directly executable Boolean operations. The conditibnal probability is used to avoid applying at each iteration the most time consuming step in reliability algorithms, which is making a set of events mutually exclusive. The algorithm has been implemented on a VAX 11/750 and can analyze fairly large networks with modest memory and time requirements.