For practical automated manufacturing systems, supervisory control techniques (SCTs) are of great significance and should be integrated in their plant models. SCTs are frequently accompanied by supervisor simplification issues. In the past, it is taken for granted that supervisor simplification is associated with systems' structure, because most simplification techniques are based on structure analysis. However, our study shows that it is actually independent from the systems' structure. This counter-intuitive statement is triggered by a simplification technique called inequality analysis, which is remarkably featured in three perspectives. First, it is a pure algebra way to simplify supervisor. Second, it can not only explain both strong and weak dependence by algebra analysis, but also the dependence that structure analysis cannot describe. Third, it is robust to inequality formation, structure change, and liveness control methods. Thanks to these features, supervisor simplification via inequality analysis becomes a systematic work irrelevant to the original systems and their liveness control. For better understanding, elementary-siphon-based technique in terms of structure analysis is utilized for comparison and discussion. Both the theoretical and experimental results validate the correctness of our statement.