We start with a combinatorial problem: determining the generating functions of certain restricted lattice walks. This can be done with support from computer algebra. The most efficient techniques are however not 'rigorous' (joint work with A. Bostan; FPSAC 2009). It is possible to make them rigorous by evaluating certain definite integrals via Zeilberger's method of creative telescoping. But the computational cost for doing so is quite high (ongoing joint work with A. Bostan, F. Chyzak, M. van Hoeij). This leads to the general question whether creative telescoping can be done in a more efficient way. In the end, we sketch an idea for minimizing the cost for creative telescoping by using a Cylindrical Decomposition computation as a preprocessing step (ongoing joint work with S. Chen).
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