  We consider a rank 1 valuation $\nu$ centered in a regular 3-dimensional
local ring $R$. We assume that the residue field $k$ of $\nu$ is contained in
$R$. An algorithm for constructing a generating sequences for $\nu$ in $R$ is
provided. This is a generalization of our previous algorithm where only
valuations of rational rank 1 were considered. We then give a comparison
example of a rational rank 3 valuation centered in a ring of polynomials in
three variables for which we explicitly compute a set of key polynomials and a
generating sequence.
