# Domains
var a1 >= -10, <= 10;
var a2 >= -10, <= 10;
var a3 >= -10, <= 10;
var x1 >= 0, <= 1;
var x2 >= 0, <= 1;
var x3 >= 0, <= 1;

# 
# ,w1 in [-1.0e8,1.0e8],
# w2 in [-1.0e8,1.0e8],
# w3 in [-1.0e8,1.0e8],
# u1 in [-1.0e8,1.0e8],
# u2 in [-1.0e8,1.0e8],
# u3 in [-1.0e8,1.0e8]
# 

# Constants
param delta := 1/30;

subject to


cons1 : a1 + a2 + a3 + 1 = 0;
cons2 : a1 + 2*a2*x1 + 3*a3*x1^2 + 4*x1^3 = 0;
cons3 : a1 + 2*a2*x2 + 3*a3*x2^2 + 4*x2^3 = 0;
cons4 : a1 + 2*a2*x3 + 3*a3*x3^2 + 4*x3^3 = 0;
cons5 : a1*(x1+x2) + a2*(x1^2 + x2^2) + a3*(x1^3 + x2^3) + x1^4 + x2^4 = 0;
cons6 : a1*(x2+x3) + a2*(x2^2 + x3^2) + a3*(x2^3 + x3^3) + x2^4 + x3^4 = 0;
cons7 : x1 + delta <= x2;
cons8 : x2 + delta <= x3;


# 
# 
# a1 + a2 + a3 + 1 = 0,
# a1*(1-3*x1^2) + a2*(2*x1-3*x1^2) - 3*x1^2 + 4*x1^3 = 0,
# a1*(1-3*x2^2) + a2*(2*x2-3*x2^2) - 3*x2^2 + 4*x2^3 = 0,
# 
# a1*(1-3*x3^2) + a2*(2*x3-3*x3^2) - 3*x3^2 + 4*x3^3 = 0,
# a1*(x1+x2-x1^3-x2^3) + a2*(x1^2+x2^2-x1^3-x2^3) - x1^3 - x2^3 + x1^4 + x2^4 = 0,
# a1*(x2+x3-x2^3-x3^3) + a2*(x2^2+x3^2-x2^3-x3^3) - x2^3 - x3^3 + x2^4 + x3^4 = 0,
# 
# x1 + delta <= x2,
# x2 + delta <= x3
# 






# 
# , x2 = 0.5
# 
# x2 = 0.5,
# a3+2=0,
# a1 = (1-sqrt(2))/2
# 


# 
# a1 + a2 + a3 + 1 = 0,
# a1 + 2*a2*x1 + 3*a3*x1^2 + 4*x1^3 = 0,
# a1 + 2*a2*x2 + 3*a3*x2^2 + 4*x2^3 = 0,
# a1 + 2*a2*x3 + 3*a3*x3^2 + 4*x3^3 = 0,
# a1*(x1+x2) + a2*(x1^2 + x2^2) + a3*(x1^3 + x2^3) + x1^4 + x2^4 = 0,
# a1*(x2+x3) + a2*(x2^2 + x3^2) + a3*(x2^3 + x3^3) + x2^4 + x3^4 = 0,
# x1 + delta <= x2,
# x2 + delta <= x3
# 




# 
# a1 + a2 + a3 + 1 = 0,
# 2*a1 + 2*a2*w1 + 3*a3*w2 + 4*w3 = 0,
# 2*a1 + 2*a2*u1 + 3*a3*u2 + 4*u3 = 0,
# a1 + 2*a2*x3 + 3*a3*x3^2 + 4*x3^3 = 0,
# a1*w1 + a2*w2 + a3*w3 + x1^4 + x2^4 = 0,
# a1*u1 + a2*u2 + a3*u3 + x2^4 + x3^4 = 0,
# w1 = x1 + x2,
# w2 = x1^2 + x2^2,
# w3 = x1^3 + x2^3,
# u1 = x3 + x2,
# u2 = x3^2 + x2^2,
# u3 = x3^3 + x2^3,
# a1 + 2*a2*x1 + 3*a3*x1^2 + 4*x1^3 = 0,
# a1 + 2*a2*x2 + 3*a3*x2^2 + 4*x2^3 = 0,
# x1 + delta <= x2,
# x2 + delta <= x3
# 



solve;
display a1, a2, a3, x1, x2, x3;