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State-of-the-art structured prediction algorithms can be applied using off-the-shelf tools by implementing a joint kernel for inputs and outputs, and an algorithm for inference. The kernel is used for mapping the data to an appropriate feature space, while the inference algorithm is used for successively adding violated constraints to the optimisation problem. While this approach leads to efficient learning algorithms for many important real world problems, there are also many cases in which successively adding violated constraints is infeasible. As a simple yet relevant problem, we consider the prediction of routes (cyclic permutations) over a given set of points of interest. Solving this problem has many potential applications. For car drivers, prediction of individual routes can be used for intelligent car sharing applications or help optimise a hybrid vehicle's charge/discharge schedule. We show that state-of-the-art structured prediction algorithms cannot guarantee polynomial runtime for this output set of cyclic permutations.