YES(?,O(n^2))

Problem:
 f(0()) -> s(0())
 f(s(0())) -> s(s(0()))
 f(s(0())) -> *(s(s(0())),f(0()))
 f(+(x,s(0()))) -> +(s(s(0())),f(x))
 f(+(x,y)) -> *(f(x),f(y))

Proof:
 Complexity Transformation Processor:
  strict:
   f(0()) -> s(0())
   f(s(0())) -> s(s(0()))
   f(s(0())) -> *(s(s(0())),f(0()))
   f(+(x,s(0()))) -> +(s(s(0())),f(x))
   f(+(x,y)) -> *(f(x),f(y))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [+](x0, x1) = x0 + x1 + 1,
     
     [*](x0, x1) = x0 + x1,
     
     [s](x0) = x0,
     
     [f](x0) = x0,
     
     [0] = 0
    orientation:
     f(0()) = 0 >= 0 = s(0())
     
     f(s(0())) = 0 >= 0 = s(s(0()))
     
     f(s(0())) = 0 >= 0 = *(s(s(0())),f(0()))
     
     f(+(x,s(0()))) = x + 1 >= x + 1 = +(s(s(0())),f(x))
     
     f(+(x,y)) = x + y + 1 >= x + y = *(f(x),f(y))
    problem:
     strict:
      f(0()) -> s(0())
      f(s(0())) -> s(s(0()))
      f(s(0())) -> *(s(s(0())),f(0()))
      f(+(x,s(0()))) -> +(s(s(0())),f(x))
     weak:
      f(+(x,y)) -> *(f(x),f(y))
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [+](x0, x1) = x0 + x1 + 1,
       
       [*](x0, x1) = x0 + x1,
       
       [s](x0) = x0,
       
       [f](x0) = x0 + 1,
       
       [0] = 1
      orientation:
       f(0()) = 2 >= 1 = s(0())
       
       f(s(0())) = 2 >= 1 = s(s(0()))
       
       f(s(0())) = 2 >= 3 = *(s(s(0())),f(0()))
       
       f(+(x,s(0()))) = x + 3 >= x + 3 = +(s(s(0())),f(x))
       
       f(+(x,y)) = x + y + 2 >= x + y + 2 = *(f(x),f(y))
      problem:
       strict:
        f(s(0())) -> *(s(s(0())),f(0()))
        f(+(x,s(0()))) -> +(s(s(0())),f(x))
       weak:
        f(0()) -> s(0())
        f(s(0())) -> s(s(0()))
        f(+(x,y)) -> *(f(x),f(y))
      Matrix Interpretation Processor:
       dimension: 2
       max_matrix:
        [1 1]
        [0 1]
        interpretation:
                       [1 1]     [1 1]     [0]
         [+](x0, x1) = [0 1]x0 + [0 1]x1 + [1],
         
                       [1 0]     [1 0]  
         [*](x0, x1) = [0 0]x0 + [0 0]x1,
         
                   [1 0]     [0]
         [s](x0) = [0 0]x0 + [1],
         
                   [1 1]  
         [f](x0) = [0 1]x0,
         
               [0]
         [0] = [1]
        orientation:
                     [1]    [1]                      
         f(s(0())) = [1] >= [0] = *(s(s(0())),f(0()))
         
                          [1 2]    [3]    [1 2]    [1]                    
         f(+(x,s(0()))) = [0 1]x + [2] >= [0 1]x + [2] = +(s(s(0())),f(x))
         
                  [1]    [0]         
         f(0()) = [1] >= [1] = s(0())
         
                     [1]    [0]            
         f(s(0())) = [1] >= [1] = s(s(0()))
         
                     [1 2]    [1 2]    [1]    [1 1]    [1 1]                
         f(+(x,y)) = [0 1]x + [0 1]y + [1] >= [0 0]x + [0 0]y = *(f(x),f(y))
        problem:
         strict:
          f(s(0())) -> *(s(s(0())),f(0()))
         weak:
          f(+(x,s(0()))) -> +(s(s(0())),f(x))
          f(0()) -> s(0())
          f(s(0())) -> s(s(0()))
          f(+(x,y)) -> *(f(x),f(y))
        Matrix Interpretation Processor:
         dimension: 2
         max_matrix:
          [1 1]
          [0 1]
          interpretation:
                                
           [+](x0, x1) = x0 + x1,
           
                         [1 0]     [1 0]  
           [*](x0, x1) = [0 0]x0 + [0 0]x1,
           
                     [1 0]     [0]
           [s](x0) = [0 0]x0 + [1],
           
                     [1 1]     [0]
           [f](x0) = [0 1]x0 + [1],
           
                 [0]
           [0] = [0]
          orientation:
                       [1]    [0]                      
           f(s(0())) = [2] >= [0] = *(s(s(0())),f(0()))
           
                            [1 1]    [1]    [1 1]    [0]                    
           f(+(x,s(0()))) = [0 1]x + [2] >= [0 1]x + [2] = +(s(s(0())),f(x))
           
                    [0]    [0]         
           f(0()) = [1] >= [1] = s(0())
           
                       [1]    [0]            
           f(s(0())) = [2] >= [1] = s(s(0()))
           
                       [1 1]    [1 1]    [0]    [1 1]    [1 1]                
           f(+(x,y)) = [0 1]x + [0 1]y + [1] >= [0 0]x + [0 0]y = *(f(x),f(y))
          problem:
           strict:
            
           weak:
            f(s(0())) -> *(s(s(0())),f(0()))
            f(+(x,s(0()))) -> +(s(s(0())),f(x))
            f(0()) -> s(0())
            f(s(0())) -> s(s(0()))
            f(+(x,y)) -> *(f(x),f(y))
          Qed