Many automatic Web testing techniques generate test cases by analyzing the GUI of the Web applications under test, aiming to exercise sequences of actions that are similar to the ones that testers could manually execute. However, the efficiency of the test generation process is severely limited by the cost of analyzing the content of the GUI screens after executing each action. In this paper, we introduce an inference component, Sibilla , which accumulates knowledge about the behavior of the GUI after each action. Sibilla enables the test generators to reuse the results computed for GUI screens that recur multiple times during the test generation process, thus improving the efficiency of Web testing techniques. We experimented Sibilla with Web testing techniques based on three different GUI exploration strategies (Random, Depth-first, and Q-learning) and nine target systems, observing reductions from 22% to 96% of the test generation time.