In this paper, we show how to implement the conformance relation on transition systems. The computability of this relation relies on the composition of two operators: the reduction relation whose computability has been proven in our previous work, and the merge function of acceptance graphs associated with transition systems under comparison. It is formally demonstrated, and illustrated through a case study whose analysis is performed by a java prototype we have developed. This research work is developed in order to be applied in a larger context: our goal is to support modelers to develop UML state machine through an incremental modelling method which is able to guarantee that model upgrading does not introduce inconsistencies. Hence, these works lead to a semantics for the specialisation relation between UML State Machines.