Abstract: Termination decision in active database is an important problem and becomes a focus for many researchers. Several works suggest proving termination by using triggering and activation graphs at compile-time, and computing an irreducible rule set is the key technique. But due to the various conservativeness of the existing approaches, the irreducible rule set computed by them can be reduced again. This defect impairs not only the correctness of termination decision at compile-time but also the efficiency of run-time rule analysis. In this paper, the characteristic of nontermination for an activation rule is analyzed in detail and such concepts as activation path, inhibited activation cycle and inhibited activation rule are proposed. Based on these concepts, an efficient algorithm for computing an irreducible rule set is presented, which can make the irreducible rule set, computed by the existing approaches, to be reduced again.