  In 1973, L.A. Levin published an algorithm that solves any inversion problem
$\pi$ as quickly as the fastest algorithm $p^*$ computing a solution for $\pi$
in time bounded by $2^{l(p^*)}.t^*$, where $l(p^*)$ is the length of the binary
encoding of $p^*$, and $t^*$ is the runtime of $p^*$ plus the time to verify
its correctness. In 2002, M. Hutter published an algorithm that solves any
well-defined problem $\pi$ as quickly as the fastest algorithm $p^*$ computing
a solution for $\pi$ in time bounded by $5.t_{p}(x)+d_p.time_{t_{p}}(x)+c_p$,
where $d_p=40.2^{l(p)+l(t_{p})}$ and $c_p=40.2^{l(f)+1}.O(l(f)^2)$, where
$l(f)$ is the length of the binary encoding of a proof $f$ that produces a pair
$(p,t_p)$, where $t_p(x)$ is a provable time bound on the runtime of the
fastest program $p$ provably equivalent to $p^*$. In this paper, we rewrite
Levin Search using the ideas of Hutter so that we have a new simple algorithm
that solves any well-defined problem $\pi$ as quickly as the fastest algorithm
$p^*$ computing a solution for $\pi$ in time bounded by $O(l(f)^2).t_p(x)$.
