YES

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:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [d](x0) = x0,
   
   [f](x0) = x0 + 5,
   
   [g](x0) = 4x0 + 4,
   
   [c](x0, x1) = x0 + 2x1 + 1,
   
   [s](x0) = x0
  orientation:
   g(c(x,s(y))) = 4x + 8y + 8 >= 4x + 8y + 8 = g(c(s(x),y))
   
   f(c(s(x),y)) = x + 2y + 6 >= x + 2y + 6 = f(c(x,s(y)))
   
   f(f(x)) = x + 10 >= x + 10 = f(d(f(x)))
   
   f(x) = x + 5 >= x = x
  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)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]  
    [d](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]     [0]
    [f](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [1],
    
              [1 0 1]  
    [g](x0) = [0 1 0]x0
              [0 0 0]  ,
    
                  [1 0 0]     [1 0 0]     [0]
    [c](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                  [0 0 0]     [0 0 1]     [0],
    
              [1 0 0]     [0]
    [s](x0) = [0 0 0]x0 + [0]
              [0 0 1]     [1]
   orientation:
                   [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]    [0]               
    g(c(x,s(y))) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = g(c(s(x),y))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]    [0]               
    
                   [1 0 0]    [1 0 0]    [0]    [1 0 0]    [1 0 0]    [0]               
    f(c(s(x),y)) = [0 0 0]x + [0 0 0]y + [0] >= [0 0 0]x + [0 0 0]y + [0] = f(c(x,s(y)))
                   [0 0 0]    [0 0 0]    [1]    [0 0 0]    [0 0 0]    [1]               
    
              [1 0 0]    [0]    [1 0 0]    [0]             
    f(f(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = f(d(f(x)))
              [0 0 0]    [1]    [0 0 0]    [1]             
   problem:
    f(c(s(x),y)) -> f(c(x,s(y)))
    f(f(x)) -> f(d(f(x)))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [d](x0) = x0,
     
     [f](x0) = 4x0 + 3,
     
     [c](x0, x1) = 2x0 + x1 + 2,
     
     [s](x0) = x0 + 2
    orientation:
     f(c(s(x),y)) = 8x + 4y + 27 >= 8x + 4y + 19 = f(c(x,s(y)))
     
     f(f(x)) = 16x + 15 >= 16x + 15 = f(d(f(x)))
    problem:
     f(f(x)) -> f(d(f(x)))
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 0 0]  
      [d](x0) = [0 0 0]x0
                [0 0 0]  ,
      
                [1 1 0]     [0]
      [f](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0]
     orientation:
                [1 1 0]    [1]    [1 1 0]    [0]             
      f(f(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = f(d(f(x)))
                [0 0 0]    [0]    [0 0 0]    [0]             
     problem:
      
     Qed