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

Proof:
 Complexity Transformation Processor:
  strict:
   f(0()) -> 0()
   f(s(x)) -> f(id(x))
   id(0()) -> 0()
   id(s(x)) -> s(id(x))
  weak:
   
  Matrix Interpretation Processor:
   dimension: 1
   max_matrix:
    1
    interpretation:
     [id](x0) = x0 + 194,
     
     [s](x0) = x0 + 82,
     
     [f](x0) = x0 + 167,
     
     [0] = 116
    orientation:
     f(0()) = 283 >= 116 = 0()
     
     f(s(x)) = x + 249 >= x + 361 = f(id(x))
     
     id(0()) = 310 >= 116 = 0()
     
     id(s(x)) = x + 276 >= x + 276 = s(id(x))
    problem:
     strict:
      f(s(x)) -> f(id(x))
      id(s(x)) -> s(id(x))
     weak:
      f(0()) -> 0()
      id(0()) -> 0()
    Matrix Interpretation Processor:
     dimension: 1
     max_matrix:
      1
      interpretation:
       [id](x0) = x0,
       
       [s](x0) = x0 + 1,
       
       [f](x0) = x0,
       
       [0] = 40
      orientation:
       f(s(x)) = x + 1 >= x = f(id(x))
       
       id(s(x)) = x + 1 >= x + 1 = s(id(x))
       
       f(0()) = 40 >= 40 = 0()
       
       id(0()) = 40 >= 40 = 0()
      problem:
       strict:
        id(s(x)) -> s(id(x))
       weak:
        f(s(x)) -> f(id(x))
        f(0()) -> 0()
        id(0()) -> 0()
      Matrix Interpretation Processor:
       dimension: 4
       max_matrix:
        [1 1 1 1]
        [0 0 0 0]
        [0 0 0 1]
        [0 0 0 1]
        interpretation:
                    [1 0 1 0]     [1]
                    [0 0 0 0]     [0]
         [id](x0) = [0 0 0 1]x0 + [0]
                    [0 0 0 1]     [0],
         
                   [1 1 1 1]     [1]
                   [0 0 0 0]     [0]
         [s](x0) = [0 0 0 1]x0 + [1]
                   [0 0 0 1]     [1],
         
                   [1 0 0 1]     [1]
                   [0 0 0 0]     [1]
         [f](x0) = [0 0 0 0]x0 + [1]
                   [0 0 0 0]     [1],
         
               [0]
               [0]
         [0] = [0]
               [0]
        orientation:
                    [1 1 1 2]    [3]    [1 0 1 2]    [2]           
                    [0 0 0 0]    [0]    [0 0 0 0]    [0]           
         id(s(x)) = [0 0 0 1]x + [1] >= [0 0 0 1]x + [1] = s(id(x))
                    [0 0 0 1]    [1]    [0 0 0 1]    [1]           
         
                   [1 1 1 2]    [3]    [1 0 1 1]    [2]           
                   [0 0 0 0]    [1]    [0 0 0 0]    [1]           
         f(s(x)) = [0 0 0 0]x + [1] >= [0 0 0 0]x + [1] = f(id(x))
                   [0 0 0 0]    [1]    [0 0 0 0]    [1]           
         
                  [1]    [0]      
                  [1]    [0]      
         f(0()) = [1] >= [0] = 0()
                  [1]    [0]      
         
                   [1]    [0]      
                   [0]    [0]      
         id(0()) = [0] >= [0] = 0()
                   [0]    [0]      
        problem:
         strict:
          
         weak:
          id(s(x)) -> s(id(x))
          f(s(x)) -> f(id(x))
          f(0()) -> 0()
          id(0()) -> 0()
        Qed