Something

f1[x_, y_] := x^3;
f2[x_, y_] := x^2*y;
f3[x_, y_] := x*y^2;
f4[x_, y_] := y^3;
g[x_, a_, {a1_, a2_, a3_, a4_, a5_, a6_, a7_, a8_}] := 
    Assuming[a >= 0 && a <= 1 && x >= 0 && x <= 1, 
      a1*f1[x, 1 - x] + a2*f2[x, 1 - x] + a3*f2[x, 1 - x] + a4*f3[x, 1 - x] + 
        a5*f2[x, 1 - x] + a6*f3[x, 1 - x] + a7*f3[x, 1 - x] + 
        a8*f4[x, 1 - x] - (a1*f1[a, 1 - a] + a2*f2[a, 1 - a] + 
            a3*f2[a, 1 - a] + a4*f3[a, 1 - a] + a5*f2[a, 1 - a] + 
            a6*f3[a, 1 - a] + a7*f3[a, 1 - a] + a8*f4[a, 1 - a])];
li = Join[Permutations[{1, 0, 0, 0, 0, 0, 0, 0}], 
      Permutations[{1, 1, 0, 0, 0, 0, 0, 0}], 
      Permutations[{1, 1, 1, 0, 0, 0, 0, 0}], 
      Permutations[{1, 1, 1, 1, 0, 0, 0, 0}], 
      Permutations[{1, 1, 1, 1, 1, 0, 0, 0}], 
      Permutations[{1, 1, 1, 1, 1, 1, 0, 0}], 
      Permutations[{1, 1, 1, 1, 1, 1, 1, 0}], 
      Permutations[{1, 1, 1, 1, 1, 1, 1, 1}]];
For[i = 1, i < 256, 
  Print[li[[i]], ": ", g[x, a, li[[i]]] // Factor, "   ", 
    If[Abs[g[0.01, 0.011, li[[i]]]]/(0.011 - 0.01) < 1, 
      "gegnbsp: 0.01 und 0.011", 
      If[Abs[g[0.91, 0.011, li[[i]]]]/(0.91 - 0.011) < 1, 
        "gegnbsp: 0.91 und 0.011", 
        If[Abs[g[0.7, 0.711, li[[i]]]]/(0.711 - 0.7) < 1, 
          "gegnbsp: 0.7 und 0.711", "kein gegenbeispiel"]]]]; i++]