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

Proof:
 Complexity Transformation Processor:
  strict:
   g(f(x),y) -> f(h(x,y))
   h(x,y) -> g(x,f(y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [h](x0, x1) = x0 + x1 + 229,
     
     [g](x0, x1) = x0 + x1 + 52,
     
     [f](x0) = x0 + 80
    orientation:
     g(f(x),y) = x + y + 132 >= x + y + 309 = f(h(x,y))
     
     h(x,y) = x + y + 229 >= x + y + 132 = g(x,f(y))
    problem:
     strict:
      g(f(x),y) -> f(h(x,y))
     weak:
      h(x,y) -> g(x,f(y))
    Matrix Interpretation Processor:
     dimension: 4
     max_matrix:
      [1 0 0 1]
      [0 0 0 1]
      [0 0 0 1]
      [0 0 0 1]
      interpretation:
                     [1 0 0 1]     [1 0 0 0]     [0]
                     [0 0 0 1]     [0 0 0 0]     [1]
       [h](x0, x1) = [0 0 0 0]x0 + [0 0 0 1]x1 + [0]
                     [0 0 0 1]     [0 0 0 0]     [0],
       
                     [1 0 0 1]     [1 0 0 0]  
                     [0 0 0 1]     [0 0 0 0]  
       [g](x0, x1) = [0 0 0 0]x0 + [0 0 0 0]x1
                     [0 0 0 1]     [0 0 0 0]  ,
       
                 [1 0 0 0]     [0]
                 [0 0 0 0]     [0]
       [f](x0) = [0 0 0 0]x0 + [0]
                 [0 0 0 1]     [1]
      orientation:
                   [1 0 0 1]    [1 0 0 0]    [1]    [1 0 0 1]    [1 0 0 0]    [0]            
                   [0 0 0 1]    [0 0 0 0]    [1]    [0 0 0 0]    [0 0 0 0]    [0]            
       g(f(x),y) = [0 0 0 0]x + [0 0 0 0]y + [0] >= [0 0 0 0]x + [0 0 0 0]y + [0] = f(h(x,y))
                   [0 0 0 1]    [0 0 0 0]    [1]    [0 0 0 1]    [0 0 0 0]    [1]            
       
                [1 0 0 1]    [1 0 0 0]    [0]    [1 0 0 1]    [1 0 0 0]             
                [0 0 0 1]    [0 0 0 0]    [1]    [0 0 0 1]    [0 0 0 0]             
       h(x,y) = [0 0 0 0]x + [0 0 0 1]y + [0] >= [0 0 0 0]x + [0 0 0 0]y = g(x,f(y))
                [0 0 0 1]    [0 0 0 0]    [0]    [0 0 0 1]    [0 0 0 0]             
      problem:
       strict:
        
       weak:
        g(f(x),y) -> f(h(x,y))
        h(x,y) -> g(x,f(y))
      Qed