# Domains
var x1 >= -4, <= 5;
var x2 >= -4, <= 5;
var x3 >= -4, <= 5;
var x4 >= -4, <= 5;
var x5 >= -4, <= 5;
var x6 >= -4, <= 5;
var x7 >= -4, <= 5;
var x8 >= -4, <= 5;
var x9 >= -4, <= 5;
var x10 >= -4, <= 5;
var x11 >= -4, <= 5;
var x12 >= -4, <= 5;
var x13 >= -4, <= 5;
var x14 >= -4, <= 5;
var x15 >= -4, <= 5;
var x16 >= -4, <= 5;
var x17 >= -4, <= 5;
var x18 >= -4, <= 5;
var x19 >= -4, <= 5;
var x20 >= -4, <= 5;
var x21 >= -4, <= 5;
var x22 >= -4, <= 5;
var x23 >= -4, <= 5;
var x24 >= -4, <= 5;
var x25 >= -4, <= 5;
var x26 >= -4, <= 5;
var x27 >= -4, <= 5;
var x28 >= -4, <= 5;
var x29 >= -4, <= 5;
var x30 >= -4, <= 5;
var x31 >= -4, <= 5;
var x32 >= -4, <= 5;
var x33 >= -4, <= 5;
var x34 >= -4, <= 5;
var x35 >= -4, <= 5;
var x36 >= -4, <= 5;
var x37 >= -4, <= 5;
var x38 >= -4, <= 5;
var x39 >= -4, <= 5;
var x40 >= -4, <= 5;
var l0 >= -1.0e16, <= 1.0e16;
var l1 >= -1.0e16, <= 1.0e16;
var l2 >= -1.0e16, <= 1.0e16;
var l3 >= -1.0e16, <= 1.0e16;
var l4 >= -1.0e16, <= 1.0e16;
var l5 >= -1.0e16, <= 1.0e16;
var l6 >= -1.0e16, <= 1.0e16;
var l7 >= -1.0e16, <= 1.0e16;
var l8 >= -1.0e16, <= 1.0e16;
var l9 >= -1.0e16, <= 1.0e16;
var l10 >= -1.0e16, <= 1.0e16;
var l11 >= -1.0e16, <= 1.0e16;
var l12 >= -1.0e16, <= 1.0e16;
var l13 >= -1.0e16, <= 1.0e16;
var l14 >= -1.0e16, <= 1.0e16;
var l15 >= -1.0e16, <= 1.0e16;
var l16 >= -1.0e16, <= 1.0e16;
var l17 >= -1.0e16, <= 1.0e16;
var l18 >= -1.0e16, <= 1.0e16;
var l19 >= -1.0e16, <= 1.0e16;
var l20 >= -1.0e16, <= 1.0e16;
var l21 >= -1.0e16, <= 1.0e16;
var l22 >= -1.0e16, <= 1.0e16;
var l23 >= -1.0e16, <= 1.0e16;
var l24 >= -1.0e16, <= 1.0e16;
var l25 >= -1.0e16, <= 1.0e16;
var l26 >= -1.0e16, <= 1.0e16;
var l27 >= -1.0e16, <= 1.0e16;
var l28 >= -1.0e16, <= 1.0e16;
var l29 >= -1.0e16, <= 1.0e16;
var l30 >= -1.0e16, <= 1.0e16;
var l31 >= -1.0e16, <= 1.0e16;
var l32 >= -1.0e16, <= 1.0e16;
var l33 >= -1.0e16, <= 1.0e16;
var l34 >= -1.0e16, <= 1.0e16;
var l35 >= -1.0e16, <= 1.0e16;
var l36 >= -1.0e16, <= 1.0e16;
var l37 >= -1.0e16, <= 1.0e16;
var l38 >= -1.0e16, <= 1.0e16;
var l39 >= -1.0e16, <= 1.0e16;
var l40 >= -1.0e16, <= 1.0e16;
var u1 >= -1.0e16, <= 1.0e16;
var u2 >= -1.0e16, <= 1.0e16;
var u3 >= -1.0e16, <= 1.0e16;
var u4 >= -1.0e16, <= 1.0e16;
var u5 >= -1.0e16, <= 1.0e16;
var u6 >= -1.0e16, <= 1.0e16;
var u7 >= -1.0e16, <= 1.0e16;
var u8 >= -1.0e16, <= 1.0e16;
var u9 >= -1.0e16, <= 1.0e16;
var u10 >= -1.0e16, <= 1.0e16;
var u11 >= -1.0e16, <= 1.0e16;
var u12 >= -1.0e16, <= 1.0e16;
var u13 >= -1.0e16, <= 1.0e16;
var u14 >= -1.0e16, <= 1.0e16;
var u15 >= -1.0e16, <= 1.0e16;
var u16 >= -1.0e16, <= 1.0e16;
var u17 >= -1.0e16, <= 1.0e16;
var u18 >= -1.0e16, <= 1.0e16;
var u19 >= -1.0e16, <= 1.0e16;
var u20 >= -1.0e16, <= 1.0e16;
var u21 >= -1.0e16, <= 1.0e16;
var u22 >= -1.0e16, <= 1.0e16;
var u23 >= -1.0e16, <= 1.0e16;
var u24 >= -1.0e16, <= 1.0e16;
var u25 >= -1.0e16, <= 1.0e16;
var u26 >= -1.0e16, <= 1.0e16;
var u27 >= -1.0e16, <= 1.0e16;
var u28 >= -1.0e16, <= 1.0e16;
var u29 >= -1.0e16, <= 1.0e16;
var u30 >= -1.0e16, <= 1.0e16;
var u31 >= -1.0e16, <= 1.0e16;
var u32 >= -1.0e16, <= 1.0e16;
var u33 >= -1.0e16, <= 1.0e16;
var u34 >= -1.0e16, <= 1.0e16;
var u35 >= -1.0e16, <= 1.0e16;
var u36 >= -1.0e16, <= 1.0e16;
var u37 >= -1.0e16, <= 1.0e16;
var u38 >= -1.0e16, <= 1.0e16;
var u39 >= -1.0e16, <= 1.0e16;
var u40 >= -1.0e16, <= 1.0e16;
var u41 >= -1.0e16, <= 1.0e16;

# Constants
param h := 1/(40+1);
param t1 := 1 * h;
param t2 := 2 * h;
param t3 := 3 * h;
param t4 := 4 * h;
param t5 := 5 * h;
param t6 := 6 * h;
param t7 := 7 * h;
param t8 := 8 * h;
param t9 := 9 * h;
param t10 := 10 * h;
param t11 := 11 * h;
param t12 := 12 * h;
param t13 := 13 * h;
param t14 := 14 * h;
param t15 := 15 * h;
param t16 := 16 * h;
param t17 := 17 * h;
param t18 := 18 * h;
param t19 := 19 * h;
param t20 := 20 * h;
param t21 := 21 * h;
param t22 := 22 * h;
param t23 := 23 * h;
param t24 := 24 * h;
param t25 := 25 * h;
param t26 := 26 * h;
param t27 := 27 * h;
param t28 := 28 * h;
param t29 := 29 * h;
param t30 := 30 * h;
param t31 := 31 * h;
param t32 := 32 * h;
param t33 := 33 * h;
param t34 := 34 * h;
param t35 := 35 * h;
param t36 := 36 * h;
param t37 := 37 * h;
param t38 := 38 * h;
param t39 := 39 * h;
param t40 := 40 * h;

subject to
cons1 : l0 = 0;
cons2 : l1 = l0 + t1*(x1+t1+1)^3;
cons3 : l2 = l1 + t2*(x2+t2+1)^3;
cons4 : l3 = l2 + t3*(x3+t3+1)^3;
cons5 : l4 = l3 + t4*(x4+t4+1)^3;
cons6 : l5 = l4 + t5*(x5+t5+1)^3;
cons7 : l6 = l5 + t6*(x6+t6+1)^3;
cons8 : l7 = l6 + t7*(x7+t7+1)^3;
cons9 : l8 = l7 + t8*(x8+t8+1)^3;
cons10 : l9 = l8 + t9*(x9+t9+1)^3;
cons11 : l10 = l9 + t10*(x10+t10+1)^3;
cons12 : l11 = l10 + t11*(x11+t11+1)^3;
cons13 : l12 = l11 + t12*(x12+t12+1)^3;
cons14 : l13 = l12 + t13*(x13+t13+1)^3;
cons15 : l14 = l13 + t14*(x14+t14+1)^3;
cons16 : l15 = l14 + t15*(x15+t15+1)^3;
cons17 : l16 = l15 + t16*(x16+t16+1)^3;
cons18 : l17 = l16 + t17*(x17+t17+1)^3;
cons19 : l18 = l17 + t18*(x18+t18+1)^3;
cons20 : l19 = l18 + t19*(x19+t19+1)^3;
cons21 : l20 = l19 + t20*(x20+t20+1)^3;
cons22 : l21 = l20 + t21*(x21+t21+1)^3;
cons23 : l22 = l21 + t22*(x22+t22+1)^3;
cons24 : l23 = l22 + t23*(x23+t23+1)^3;
cons25 : l24 = l23 + t24*(x24+t24+1)^3;
cons26 : l25 = l24 + t25*(x25+t25+1)^3;
cons27 : l26 = l25 + t26*(x26+t26+1)^3;
cons28 : l27 = l26 + t27*(x27+t27+1)^3;
cons29 : l28 = l27 + t28*(x28+t28+1)^3;
cons30 : l29 = l28 + t29*(x29+t29+1)^3;
cons31 : l30 = l29 + t30*(x30+t30+1)^3;
cons32 : l31 = l30 + t31*(x31+t31+1)^3;
cons33 : l32 = l31 + t32*(x32+t32+1)^3;
cons34 : l33 = l32 + t33*(x33+t33+1)^3;
cons35 : l34 = l33 + t34*(x34+t34+1)^3;
cons36 : l35 = l34 + t35*(x35+t35+1)^3;
cons37 : l36 = l35 + t36*(x36+t36+1)^3;
cons38 : l37 = l36 + t37*(x37+t37+1)^3;
cons39 : l38 = l37 + t38*(x38+t38+1)^3;
cons40 : l39 = l38 + t39*(x39+t39+1)^3;
cons41 : l40 = l39 + t40*(x40+t40+1)^3;
cons42 : u41 = 0;
cons43 : u1 = u2 + (1-t1)*(x1+t1+1)^3;
cons44 : u2 = u3 + (1-t2)*(x2+t2+1)^3;
cons45 : u3 = u4 + (1-t3)*(x3+t3+1)^3;
cons46 : u4 = u5 + (1-t4)*(x4+t4+1)^3;
cons47 : u5 = u6 + (1-t5)*(x5+t5+1)^3;
cons48 : u6 = u7 + (1-t6)*(x6+t6+1)^3;
cons49 : u7 = u8 + (1-t7)*(x7+t7+1)^3;
cons50 : u8 = u9 + (1-t8)*(x8+t8+1)^3;
cons51 : u9 = u10 + (1-t9)*(x9+t9+1)^3;
cons52 : u10 = u11 + (1-t10)*(x10+t10+1)^3;
cons53 : u11 = u12 + (1-t11)*(x11+t11+1)^3;
cons54 : u12 = u13 + (1-t12)*(x12+t12+1)^3;
cons55 : u13 = u14 + (1-t13)*(x13+t13+1)^3;
cons56 : u14 = u15 + (1-t14)*(x14+t14+1)^3;
cons57 : u15 = u16 + (1-t15)*(x15+t15+1)^3;
cons58 : u16 = u17 + (1-t16)*(x16+t16+1)^3;
cons59 : u17 = u18 + (1-t17)*(x17+t17+1)^3;
cons60 : u18 = u19 + (1-t18)*(x18+t18+1)^3;
cons61 : u19 = u20 + (1-t19)*(x19+t19+1)^3;
cons62 : u20 = u21 + (1-t20)*(x20+t20+1)^3;
cons63 : u21 = u22 + (1-t21)*(x21+t21+1)^3;
cons64 : u22 = u23 + (1-t22)*(x22+t22+1)^3;
cons65 : u23 = u24 + (1-t23)*(x23+t23+1)^3;
cons66 : u24 = u25 + (1-t24)*(x24+t24+1)^3;
cons67 : u25 = u26 + (1-t25)*(x25+t25+1)^3;
cons68 : u26 = u27 + (1-t26)*(x26+t26+1)^3;
cons69 : u27 = u28 + (1-t27)*(x27+t27+1)^3;
cons70 : u28 = u29 + (1-t28)*(x28+t28+1)^3;
cons71 : u29 = u30 + (1-t29)*(x29+t29+1)^3;
cons72 : u30 = u31 + (1-t30)*(x30+t30+1)^3;
cons73 : u31 = u32 + (1-t31)*(x31+t31+1)^3;
cons74 : u32 = u33 + (1-t32)*(x32+t32+1)^3;
cons75 : u33 = u34 + (1-t33)*(x33+t33+1)^3;
cons76 : u34 = u35 + (1-t34)*(x34+t34+1)^3;
cons77 : u35 = u36 + (1-t35)*(x35+t35+1)^3;
cons78 : u36 = u37 + (1-t36)*(x36+t36+1)^3;
cons79 : u37 = u38 + (1-t37)*(x37+t37+1)^3;
cons80 : u38 = u39 + (1-t38)*(x38+t38+1)^3;
cons81 : u39 = u40 + (1-t39)*(x39+t39+1)^3;
cons82 : u40 = u41 + (1-t40)*(x40+t40+1)^3;
cons83 : 0 = x1+0.5*h*((1-t1)*l1 + t1*u2);
cons84 : 0 = x2+0.5*h*((1-t2)*l2 + t2*u3);
cons85 : 0 = x3+0.5*h*((1-t3)*l3 + t3*u4);
cons86 : 0 = x4+0.5*h*((1-t4)*l4 + t4*u5);
cons87 : 0 = x5+0.5*h*((1-t5)*l5 + t5*u6);
cons88 : 0 = x6+0.5*h*((1-t6)*l6 + t6*u7);
cons89 : 0 = x7+0.5*h*((1-t7)*l7 + t7*u8);
cons90 : 0 = x8+0.5*h*((1-t8)*l8 + t8*u9);
cons91 : 0 = x9+0.5*h*((1-t9)*l9 + t9*u10);
cons92 : 0 = x10+0.5*h*((1-t10)*l10 + t10*u11);
cons93 : 0 = x11+0.5*h*((1-t11)*l11 + t11*u12);
cons94 : 0 = x12+0.5*h*((1-t12)*l12 + t12*u13);
cons95 : 0 = x13+0.5*h*((1-t13)*l13 + t13*u14);
cons96 : 0 = x14+0.5*h*((1-t14)*l14 + t14*u15);
cons97 : 0 = x15+0.5*h*((1-t15)*l15 + t15*u16);
cons98 : 0 = x16+0.5*h*((1-t16)*l16 + t16*u17);
cons99 : 0 = x17+0.5*h*((1-t17)*l17 + t17*u18);
cons100 : 0 = x18+0.5*h*((1-t18)*l18 + t18*u19);
cons101 : 0 = x19+0.5*h*((1-t19)*l19 + t19*u20);
cons102 : 0 = x20+0.5*h*((1-t20)*l20 + t20*u21);
cons103 : 0 = x21+0.5*h*((1-t21)*l21 + t21*u22);
cons104 : 0 = x22+0.5*h*((1-t22)*l22 + t22*u23);
cons105 : 0 = x23+0.5*h*((1-t23)*l23 + t23*u24);
cons106 : 0 = x24+0.5*h*((1-t24)*l24 + t24*u25);
cons107 : 0 = x25+0.5*h*((1-t25)*l25 + t25*u26);
cons108 : 0 = x26+0.5*h*((1-t26)*l26 + t26*u27);
cons109 : 0 = x27+0.5*h*((1-t27)*l27 + t27*u28);
cons110 : 0 = x28+0.5*h*((1-t28)*l28 + t28*u29);
cons111 : 0 = x29+0.5*h*((1-t29)*l29 + t29*u30);
cons112 : 0 = x30+0.5*h*((1-t30)*l30 + t30*u31);
cons113 : 0 = x31+0.5*h*((1-t31)*l31 + t31*u32);
cons114 : 0 = x32+0.5*h*((1-t32)*l32 + t32*u33);
cons115 : 0 = x33+0.5*h*((1-t33)*l33 + t33*u34);
cons116 : 0 = x34+0.5*h*((1-t34)*l34 + t34*u35);
cons117 : 0 = x35+0.5*h*((1-t35)*l35 + t35*u36);
cons118 : 0 = x36+0.5*h*((1-t36)*l36 + t36*u37);
cons119 : 0 = x37+0.5*h*((1-t37)*l37 + t37*u38);
cons120 : 0 = x38+0.5*h*((1-t38)*l38 + t38*u39);
cons121 : 0 = x39+0.5*h*((1-t39)*l39 + t39*u40);
cons122 : 0 = x40+0.5*h*((1-t40)*l40 + t40*u41);

solve;
display l0, l1, l10, l11, l12, l13, l14, l15, l16, l17, l18, l19, l2, l20, l21, l22, l23, l24, l25, l26, l27, l28, l29, l3, l30, l31, l32, l33, l34, l35, l36, l37, l38, l39, l4, l40, l5, l6, l7, l8, l9, u1, u10, u11, u12, u13, u14, u15, u16, u17, u18, u19, u2, u20, u21, u22, u23, u24, u25, u26, u27, u28, u29, u3, u30, u31, u32, u33, u34, u35, u36, u37, u38, u39, u4, u40, u41, u5, u6, u7, u8, u9, x1, x10, x11, x12, x13, x14, x15, x16, x17, x18, x19, x2, x20, x21, x22, x23, x24, x25, x26, x27, x28, x29, x3, x30, x31, x32, x33, x34, x35, x36, x37, x38, x39, x4, x40, x5, x6, x7, x8, x9;