YES(?,O(n^2))

Problem:
 f(0()) -> s(0())
 f(s(x)) -> g(s(s(x)))
 g(0()) -> s(0())
 g(s(0())) -> s(0())
 g(s(s(x))) -> f(x)

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