Termination of active rule set is one of the three important characteristics of active database rule sets. It will directly influence the application of active database systems. By analysis of dependency relationship, which exists among the active rules, such concepts are given as triggering-transition closure, dependency-transition closure etc. Based on these concepts, an approach is supposed to analyze termination of active rule set by triggering-dependency graph (T-DG) of active rules. Especially, the approach deciding termination of the active rule set corresponding to a triggering-graph (TG) is studied, which includes a cycle. Also given are the corresponding deciding algorithms, verification and analysis of the algorithms.