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This paper is concerned with the construction of a fast algorithm forcomputing the maximum speed of propagation in the Riemann solution for theEuler system of gas dynamics with the co-volume equation of state. The noveltyin the algorithm is that it stops when a guaranteed upper bound for the maximumspeed is reached with a prescribed accuracy. The convergence rate of thealgorithm is cubic and the bound is guaranteed for gasses with the co-volumeequation of state and the heat capacity ratio $\gamma$ in the range $(1,5/3]$

Fast estimation from above of the maximum wave speed in the Riemann problem for the Euler equations