Re-expressing a function

Question

Is it possible to re-express the function $$ f(t+x_1,t+x_2,x_1,x_2)=x_1+x_2+t $$ as $f(y_1,y_2,y_3,y_4)=???$

Answer 1

We could have $f(y_1, y_2, y_3, y_4) = y_1 + y_4$ or $f(y_1, y_2, y_3, y_4) = y_2 + y_3$ so there is no unique solution. Infinitely many solutions can be found of the form $ay_1 + (1-a)y_2 + (1-a)y_3 + ay_4$ for constant $a$. However, there exist solutions that are not of this form.