Summary: Let \(\alpha=(1+\sqrt{2})/2\) and define the lower and upper Wythoff sequences by \(ai = \lfloor{ i\alpha\rfloor},b_i=\lfloor i\alpha^2\rfloor\) for \(i\ge 1\). In a recent interesting paper, S. Kawsumarng et al. [Period. Math. Hung. 82, No. 1, 98–113 (2021; Zbl 1474.11033)] proved a number of results about numbers representable as sums of the form \(a_i +a_j\), \(b_i +b_j\), \(a_i +b_j\), and so forth. In this paper I show how to derive all of their results, using one simple idea and existing free software called Walnut. The key idea is that for each of their sumsets, there is a relatively small automaton accepting the Fibonacci representation of the numbers represented. I also show how the automaton approach can easily prove other results.