  The type IIB matrix model was proposed as a non-perturbative formulation of
superstring theory in 1996. We simulate a model that describes the late time
behavior of the IIB matrix model by applying the complex Langevin method to
overcome the sign problem. We clarify the relationship between the Euclidean
and the Lorentzian versions of the type IIB matrix model in a recently
discovered phase. By introducing a constraint, we obtain a model where the
spacetime metric is Euclidean at early times, whereas it {\it dynamically}
becomes Lorentzian at late times.
