  Anderson proved that the finite generation of the value semigroup
$\Gamma_{Y_\bullet}(D)$ in the construction of the Newton-Okounkov body
$\Delta_{Y_\bullet}(D)$ induces a toric degeneration of the corresponding
variety $X$ to some toric variety $X_0$. In this case the normalization of
$X_0$ is the normal toric variety corresponding to the rational polytope
$\Delta_{Y_\bullet}(D)$. Since $X_0$ is not normal in general this
correspondence is rather implicit. In this article we investigate in conditions
to assure that $X_0$ is normal, by comparing the Hilbert polynomial with the
Ehrhart polynomial.
  In the case of del Pezzo surfaces this will result in an algorithm which
outputs for a given divisor $D$ a flag $Y_\bullet$ such that the value
semigroup in question is indeed normal. Furthermore, we will find flags on del
Pezzo surfaces and on some particular weak del Pezzo surfaces which induce
normal toric degenerations for all possible divisors at once. We will prove
that in this case the global value semigroup $\Gamma_{Y_\bullet}(X)$ is
finitely generated and normal.
