YES(?,O(n^2))

Problem:
 f(a()) -> f(b())
 g(b()) -> g(a())

Proof:
 Complexity Transformation Processor:
  strict:
   f(a()) -> f(b())
   g(b()) -> g(a())
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [g](x0) = x0,
     
     [b] = 1,
     
     [f](x0) = x0,
     
     [a] = 0
    orientation:
     f(a()) = 0 >= 1 = f(b())
     
     g(b()) = 1 >= 0 = g(a())
    problem:
     strict:
      f(a()) -> f(b())
     weak:
      g(b()) -> g(a())
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 0]
      interpretation:
                 [1 0]     [1]
       [g](x0) = [0 0]x0 + [1],
       
             [0]
       [b] = [0],
       
                 [1 1]  
       [f](x0) = [0 0]x0,
       
             [0]
       [a] = [1]
      orientation:
                [1]    [0]         
       f(a()) = [0] >= [0] = f(b())
       
                [1]    [1]         
       g(b()) = [1] >= [1] = g(a())
      problem:
       strict:
        
       weak:
        f(a()) -> f(b())
        g(b()) -> g(a())
      Qed