This paper presents an efficient test that uses abstractions to detect conflict in composed systems controlled by local supervisors. This test, called nonconflict test, is not applied over the languages generated by the supervisors, but over abstractions of the supervisors with some specific characteristics. The concept of observer and the definition of the set of relevant events are the basis for the approach. Two strategies to define the set of relevant events are presented, along with illustrative examples. The paper also introduces a combined strategy, which consists of applying the two strategies in sequence leading, in many cases, to better reductions than when applying each strategy independently. An example is presented to illustrate the combined strategy.