  For years limited Monte Carlo simulations have led to the suspicion that the
time to failure of hierarchically organized load-transfer models of fracture is
non-zero for sets of infinite size. This fact could have a profound
significance in engineering practice and also in geophysics. Here, we develop
an exact algebraic iterative method to compute the successive time intervals
for individual breaking in systems of height $n$ in terms of the information
calculated in the previous height $n-1$. As a byproduct of this method,
rigorous lower and higher bounds for the time to failure of very large systems
are easily obtained. The asymptotic behavior of the resulting lower bound leads
to the evidence that the above mentioned suspicion is actually true.
