Supporting active rules has become an important characteristic of modern database systems. While active rules termination is an undecidable problem, several recent works have suggested proving termination by using triggering and activation graphs. In this paper, we propose such concepts as activation reachable, activation path, inhibited activation cycle, inhibited activation rule, effective activation path to refine these works. Based on these concepts and the formula constructed for an effective activation path, we show how to determine the termination of active rules set. The analytical results prove that our approach can detect more termination situations than existing works. Moveover, the proposed approach is practical and general with respect to the various rule languages from Event-Condition-Action language for XML to the trigger language in SQL: 1999 standard. As a result, it can be easily applied to modern database systems.