YES(?,O(n^2))

Problem:
 g(c(x,s(y))) -> g(c(s(x),y))
 f(c(s(x),y)) -> f(c(x,s(y)))
 f(f(x)) -> f(d(f(x)))
 f(x) -> x

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