  We consider the $X$-Greedy Algorithm and the Dual Greedy Algorithm in a
finite-dimensional Banach space with a strictly monotone basis as the
dictionary. We show that when the dictionary is an initial segment of the Haar
basis in $L_p[0,1]$ ($1 < p < \infty$) then the algorithms terminate after
finitely many iterations and that the number of iterations is bounded by a
function of the length of the initial segment. We also prove a more general
result for a class of strictly monotone bases.
