YES(?,O(n^2))

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

Proof:
 Complexity Transformation Processor:
  strict:
   g(s(x)) -> f(x)
   f(0()) -> s(0())
   f(s(x)) -> s(s(g(x)))
   g(0()) -> 0()
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [0] = 1,
     
     [f](x0) = x0,
     
     [g](x0) = x0 + 1,
     
     [s](x0) = x0 + 1
    orientation:
     g(s(x)) = x + 2 >= x = f(x)
     
     f(0()) = 1 >= 2 = s(0())
     
     f(s(x)) = x + 1 >= x + 3 = s(s(g(x)))
     
     g(0()) = 2 >= 1 = 0()
    problem:
     strict:
      f(0()) -> s(0())
      f(s(x)) -> s(s(g(x)))
     weak:
      g(s(x)) -> f(x)
      g(0()) -> 0()
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [0] = 1,
       
       [f](x0) = x0 + 1,
       
       [g](x0) = x0 + 1,
       
       [s](x0) = x0
      orientation:
       f(0()) = 2 >= 1 = s(0())
       
       f(s(x)) = x + 1 >= x + 1 = s(s(g(x)))
       
       g(s(x)) = x + 1 >= x + 1 = f(x)
       
       g(0()) = 2 >= 1 = 0()
      problem:
       strict:
        f(s(x)) -> s(s(g(x)))
       weak:
        f(0()) -> s(0())
        g(s(x)) -> f(x)
        g(0()) -> 0()
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
               [1]
         [0] = [1],
         
                   [1 1]     [0]
         [f](x0) = [0 1]x0 + [1],
         
                   [1 1]  
         [g](x0) = [0 1]x0,
         
                        [0]
         [s](x0) = x0 + [1]
        orientation:
                   [1 1]    [1]    [1 1]    [0]             
         f(s(x)) = [0 1]x + [2] >= [0 1]x + [2] = s(s(g(x)))
         
                  [2]    [1]         
         f(0()) = [2] >= [2] = s(0())
         
                   [1 1]    [1]    [1 1]    [0]       
         g(s(x)) = [0 1]x + [1] >= [0 1]x + [1] = f(x)
         
                  [2]    [1]      
         g(0()) = [1] >= [1] = 0()
        problem:
         strict:
          
         weak:
          f(s(x)) -> s(s(g(x)))
          f(0()) -> s(0())
          g(s(x)) -> f(x)
          g(0()) -> 0()
        Qed