Question: why relative rank is 2 but LgLf3h is not 0

restart;

Lfh := proc(numoflevel, h, fx, var)

if numoflevel = 1 then

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(h[i], var[i])*fx[i];

        od;

        return hello;

else

        hello := 0;

        for i from 1 to nops(var) do

                hello := hello + diff(Lfh(numoflevel-1, h, fx, var), var[i])*fx[i];

        od;

        return hello;

end if;

end proc:

f:=[x3-x2^3,-x2,x1^2-x3];

g:=[0,-1,1];

h:=[x1,0,0];

variables := [x1,x2,x3];

Lf1h := Lfh(1,h,f,variables);

Lgf1h := Lfh(1,[seq(Lf1h,n=1..nops(variables))],g,variables);

Lf2h := Lfh(2,h,f,variables);

Lgf2h := Lfh(1,[seq(Lf2h,n=1..nops(variables))],g,variables);

Lf3h := Lfh(3,h,f,variables);

Lgf3h := Lfh(1,[seq(Lf3h,n=1..nops(variables))],g,variables);

i doubt that my book example is wrong

it said relative rank is 2, but i can not find any zero when Lgf3h

if i continue to Lgf4h, Lgf5h, Lgf6h...etc, still no zero what does it mean?