We study changes of variable, called time transformations, which reduce a
delay differential equation (DDE) with a variable non-vanishing delay and an unbounded lag function to another DDE with
a constant delay. By using this reduction, we can easily obtain a
superconvergent integration of the original equation, even in the case of a
non-strictly-increasing lag function, and study the type of decay to zero of
solutions of scalar linear non-autonomous equations with a strictly
increasing lag function.