Suppose I have a system of $2^{2^{n(n-1)}}-2$ equations and I show that it is equivalent to a system of $n\times (2^{2^{n-1}}-2)$ equations.
Is there any synthetic notion that can capture such a reduction?
I understand that we cannot use the "order of computational complexity" notion as I haven't said anything about the characteristics of the equations, but I was wondering whether there is something similar that can help here.