Symbolic terminal reliability algorithms are important for analysis and synthesis of computer networks. The authors 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 disinct approach in which most of the computations performed are directly executable Boolean operations. The conditional probability is used to avoid applying at each iteration the most time-consuming loop in reliability algorithms (making a set of events mutually exclusive). The algorithm has been implemented on a VAX-11/750 and is efficient compared to existing reliability algorithms.