Here is an example from Ezra Miller's book: *Combinatorial Commutative Algebra*,p26-27

Let $f,g\in k[x_1,x_2,x_3,x_4]$ be a generic forms of degree $d$ and $e$, the *generic initial ideal* of $I=\langle f,g\rangle$ for both the *lexicographic order* and the *inverse lexicographic order*.  
When $(d,e)=(2,2)$,the ideals $J=\operatorname{gin}_{\operatorname{lex}}(I)$ are $(x_2^4,x_1x_3^2,x_1x_2,x_1^2)$, 
the ideal $J=\operatorname{gin}_{\operatorname{revlex}}(I)$ are $(x_2^3,x_1x_2,x_1^2)$.

How to find it?