We study the complexity of Gröbner bases computation, in particular in the generic situation where the variables are in simultaneous Noether position with respect to the system. We bound precisely the exponent of the complexity of Faugère F5 algorithm in this case. This complexity is related to the index of regularity of the ideal. For regular systems, this index is well- known. We define a class of overdetermined systems called semi- regular systems for which we derive sharp asymptotic estimates of the index of regularity. These systems are conjectured to be generic in a precise sense. This is joint work with Magali Bardet and Jean-Charles Faugère.