CVXPY
Minimize
  x
Subject To
 33: 1.0 <= minimum(x + 1.0, 2.0)
Bounds
 x free
End
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AFTER COMPILATION
Minimize
  C0
Subject To
 R0: - C0 - C1 <= 1
 R1: - C1 <= 2
 R2: C1 <= -1
Bounds
 C0 free
 C1 free
End
----------------------------------------
GUROBI
Minimize
  x
Subject To
 R0: - x + AddExpression_1 = 1
 33: minimum_2 >= 1
Bounds
 x free
 AddExpression_1 free
 minimum_2 free
General Constraints
 GC0: minimum_2 = MIN ( AddExpression_1 , 2 )
End