We present a simple exact algorithm for the \is\ problem with a runtime bounded

by $O(\rt^n \poly(n))$. This bound is obtained by, firstly, applying a new

branching rule and, secondly, by a distinct, computer-aided case analysis.

The new branching rule uses the concept of satellites and has previously only

been used in an algorithm for sparse graphs.

The computer-aided case analysis allows us to capture the behavior of our algorithm

in more detail than in a traditional analysis.

The main purpose of this paper is to demonstrate how a very simple

algorithm can outperform more complicated ones if the right analysis

of its running time is performed.