YES

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

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 0 0]     [1 0 0]  
   [c](x0, x1) = [0 1 1]x0 + [0 0 0]x1
                 [0 0 0]     [0 0 0]  ,
   
             [1 0 0]  
   [g](x0) = [0 0 0]x0
             [0 0 0]  ,
   
             [1 0 0]     [0]
   [s](x0) = [0 1 1]x0 + [0]
             [0 0 0]     [1],
   
             [1 1 0]  
   [f](x0) = [0 1 0]x0
             [0 0 0]  
  orientation:
                  [1 1 1]    [1 0 0]    [1]    [1 1 1]    [1 0 0]                
   f(c(s(x),y)) = [0 1 1]x + [0 0 0]y + [1] >= [0 1 1]x + [0 0 0]y = f(c(x,s(y)))
                  [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
   
                  [1 0 0]    [1 0 0]     [1 0 0]    [1 0 0]                
   g(c(x,s(y))) = [0 0 0]x + [0 0 0]y >= [0 0 0]x + [0 0 0]y = g(c(s(x),y))
                  [0 0 0]    [0 0 0]     [0 0 0]    [0 0 0]                
  problem:
   g(c(x,s(y))) -> g(c(s(x),y))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [c](x0, x1) = 3x0 + 4x1 + 2,
    
    [g](x0) = x0 + 4,
    
    [s](x0) = x0 + 4
   orientation:
    g(c(x,s(y))) = 3x + 4y + 22 >= 3x + 4y + 18 = g(c(s(x),y))
   problem:
    
   Qed