  An integral equation is a way to encapsulate the relationships between a
function and its integrals. We develop a systematic way of describing Volterra
integral equations -- specifically an algorithm that reduces any separable
Volterra integral equation into an equivalent one in operator-linear form, i.e.
one that only contains iterated integrals. This serves to standardize the
presentation of such integral equations so as to only consider those containing
iterated integrals. We use the algebraic object of the integral operator, the
twisted Rota-Baxter identity, and vertex-edge decorated rooted trees to
construct our algorithm.
