  We extend the integrability analysis for scalar evolution equations of type
$$u_t=u_m+f(u,u_1,...,u_{m-1})$$ from the case that the right hand side is a
$\lambda$-homogeneous formal power series to the case that it is a
nonhomogeneous formal power series. It is proved that the existence of one
nontrivial symmetry implies the existence of infinitely many, more precisely,
the orders of the infinite integrable hierarchy must be one of the following
cases: $\mathbb{Z}_++1$, $2\mathbb{Z}_++1$, $6\mathbb{Z}_+\pm1$, or
$6\mathbb{Z}_++1$. Moreover, if the nonlinear part of the equation is a
polynomial of order less than $m-1$, we show that any generalized symmetry is
also of polynomial type.
