  To a generically big adelic divisor, we can associate an arithmetic Okounkov
body, which is a pair of the geometric Okounkov body and the concave transform
of the Green functions. In this paper, we show that the infimum of the concave
transform is given by the absolute minimum provided that the divisor is
vertically nef. This is a partial generalization of results of Moriwaki (in the
curve case) and of Burgos Gil-Moriwaki-Philippon-Sombra (in the toric case).
