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Social norms can help solving cooperation dilemmas, constituting a key ingredient in systems of indirect reciprocity (IR). Under IR, agents are associated with different reputations, whose attribution depends on socially adopted norms that judge behaviors as good or bad. While the pros and cons of having a certain public image depend on how agents learn to discriminate between reputations, the mechanisms incentivizing agents to report the outcome of their interactions remain unclear, especially when reporting involves a cost (costly reputation building). Here we develop a new model---inspired in evolutionary game theory---and show that two social norms can sustain high levels of cooperation, even if reputation building is costly. For that, agents must be able to anticipate the reporting intentions of their opponents. Cooperation depends sensitively on both the cost of reporting and the accuracy level of reporting anticipation.