# Simplify (or Reduce) a system of inequalities intelligently

I have the following system of inequalities of 4 real variables

3 (a + b) + 4 (d + c) > 0 && 2 (a - d) + 3 (b - c) > 0


The system can be written as a system of 3 independent variables using the following variables

a+b=x
d+c=y
a-d=e
b-c=x-y-e

3x+4y>0 && -e +3(x-y)>0


Is there a way to do this simplification without telling Mathematica how to redefine the variables?

I know that I can use Assumptions->{...} to simplify the expression by enforcing the redefinitions. But I want something more.

I would like to know if Mathematica is able to identify which are the independent variables of a system of inequalities (even more difficult than the one I am considering).