By non-trivial algorithm, I mean anything besides the trivial "do nothing" algorithm that simply terminates.
This is pretty trivial, but don't algorithms require a notion of monotonic time?
From what I understand, all computation requires a sort of reduction step, from the reduction of the transition function in Turing machines to the types of reduction within lambda calculus. But having reduction requires a notion of change itself means that a change of state must be defined with respect to a change in some constant unit of change that is uniform.
Whether that notion of change is the steady rate of change of the instruction count register of a computer or the steps in the reduction of a formula to normal form, does every single type of computation require a notion of change, and, therefore, "time" as a sort of immutable, constant, and uni-directional measure of change?