Do algorithms reduce?
A reduction can be thought of a way to "rephrase" a problem in terms
of another. This can be denoted using $A \to B$, $A$ reduces to
$B$. This means that if you have an algorithm that solves $B$
then you also have an algorithm that solves $A$, since $A$ reduces
to $B$, $A \to B$. Now you also have $B \to A$ so in some way, your
problems are equivalent since they can be reduced to each other.

However, this does not imply much about the algorithms themselves
because they can be arbitrarily bad. For example, the sorting problem
has time complexity $O(n \log n)$. But an awful algorithm that sorts by
testing all possible permutations has time complexity $O(n!)$.

The only thing we can say is that the algorithms aren't better (their
time complexity isn't lower than) the problems themselves.