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.
