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Using graph transformation as a formalism to specify model transformation, termination and confluence of the graph transformation system are often required properties. Only under these two conditions, existence and uniqueness of the outcoming model is ensured. Verifying confluence of a graph transformation system can be reduced to checking both local confluence and termination. A graph transformation system is locally confluent, if all its conflicts in a minimal context can be resolved. Formally, this means, that all critical pairs of the graph transformation system should be strictly confluent. Thus, answering the question of local confluence of a graph transformation system, requires the following two steps. At first the computation of all critical pairs is necessary. Secondly this set of critical pairs has to be tested for strict confluence. This paper concentrates on the first step, proposing an efficient method to compute the set of all critical pairs of a given graph transformation system. Efficiency is obtained because of the following two main reasons. At first all pairs of rules are analyzed to check if they can actually cause a conflict. Then for each conflict inducing pair of rules, the set of critical pairs is computed in a constructive way, avoiding needless computations. The overall goal of this paper is to encourage tool development and enhancement concerning the detection of conflicts in a graph transformation system. It should be an aid to translate the main theoretical results concerning confluence of a graph transformation system into practical methods for the analysis of model transformations specified with graph transformation.