YES(?,O(n^2))

Problem:
 f(x,y) -> g(x,y)
 g(h(x),y) -> h(f(x,y))
 g(h(x),y) -> h(g(x,y))

Proof:
 Complexity Transformation Processor:
  strict:
   f(x,y) -> g(x,y)
   g(h(x),y) -> h(f(x,y))
   g(h(x),y) -> h(g(x,y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [h](x0) = x0,
     
     [g](x0, x1) = x0 + x1,
     
     [f](x0, x1) = x0 + x1 + 1
    orientation:
     f(x,y) = x + y + 1 >= x + y = g(x,y)
     
     g(h(x),y) = x + y >= x + y + 1 = h(f(x,y))
     
     g(h(x),y) = x + y >= x + y = h(g(x,y))
    problem:
     strict:
      g(h(x),y) -> h(f(x,y))
      g(h(x),y) -> h(g(x,y))
     weak:
      f(x,y) -> g(x,y)
    Matrix Interpretation Processor:
     dimension: 2
     max_matrix:
      [1 1]
      [0 1]
      interpretation:
                      [1]
       [h](x0) = x0 + [1],
       
                     [1 1]     [1 0]  
       [g](x0, x1) = [0 1]x0 + [0 0]x1,
       
                     [1 1]     [1 0]     [1]
       [f](x0, x1) = [0 1]x0 + [0 0]x1 + [0]
      orientation:
                   [1 1]    [1 0]    [2]    [1 1]    [1 0]    [2]            
       g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(f(x,y))
       
                   [1 1]    [1 0]    [2]    [1 1]    [1 0]    [1]            
       g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(g(x,y))
       
                [1 1]    [1 0]    [1]    [1 1]    [1 0]          
       f(x,y) = [0 1]x + [0 0]y + [0] >= [0 1]x + [0 0]y = g(x,y)
      problem:
       strict:
        g(h(x),y) -> h(f(x,y))
       weak:
        g(h(x),y) -> h(g(x,y))
        f(x,y) -> g(x,y)
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
                        [0]
         [h](x0) = x0 + [1],
         
                       [1 1]     [1 1]  
         [g](x0, x1) = [0 1]x0 + [0 0]x1,
         
                       [1 1]     [1 1]  
         [f](x0, x1) = [0 1]x0 + [0 0]x1
        orientation:
                     [1 1]    [1 1]    [1]    [1 1]    [1 1]    [0]            
         g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(f(x,y))
         
                     [1 1]    [1 1]    [1]    [1 1]    [1 1]    [0]            
         g(h(x),y) = [0 1]x + [0 0]y + [1] >= [0 1]x + [0 0]y + [1] = h(g(x,y))
         
                  [1 1]    [1 1]     [1 1]    [1 1]          
         f(x,y) = [0 1]x + [0 0]y >= [0 1]x + [0 0]y = g(x,y)
        problem:
         strict:
          
         weak:
          g(h(x),y) -> h(f(x,y))
          g(h(x),y) -> h(g(x,y))
          f(x,y) -> g(x,y)
        Qed