CVXPY
Maximize
  Sum(X, None, False)
Subject To
 26: max(X, None, False) + max(Y, None, False) <= 1.0
 31: Y == 1.0
Bounds
 X free
 Y free
End
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AFTER COMPILATION
Minimize
  - x_0 - x_1 - x_2 - x_3
Subject To
 R0: x_5 = 1
 R1: x_6 = 1
 R2: x_7 = 1
 R3: x_8 = 1
 R4: x_0 - x_4 <= 0
 R5: x_1 - x_4 <= 0
 R6: x_2 - x_4 <= 0
 R7: x_3 - x_4 <= 0
 R8: x_5 - x_9 <= 0
 R9: x_6 - x_9 <= 0
 R10: x_7 - x_9 <= 0
 R11: x_8 - x_9 <= 0
 R12: x_4 + x_9 <= 1
Bounds
 x_0 free
 x_1 free
 x_2 free
 x_3 free
 x_4 free
 x_5 free
 x_6 free
 x_7 free
 x_8 free
 x_9 free
End
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GUROBI
Maximize
  X[0,0] + X[0,1] + X[1,0] + X[1,1]
Subject To
 26: max_1 + max_2 <= 1
 31[0,0]: Y[0,0] = 1
 31[0,1]: Y[0,1] = 1
 31[1,0]: Y[1,0] = 1
 31[1,1]: Y[1,1] = 1
Bounds
 X[0,0] free
 X[0,1] free
 X[1,0] free
 X[1,1] free
 max_1 free
 Y[0,0] free
 Y[0,1] free
 Y[1,0] free
 Y[1,1] free
 max_2 free
General Constraints
 GC0: max_1 = MAX ( X[0,0] , X[0,1] , X[1,0] , X[1,1] )
 GC1: max_2 = MAX ( Y[0,0] , Y[0,1] , Y[1,0] , Y[1,1] )
End