YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [c](x0, x1) = 4x0 + 4x1,
   
   [g](x0) = x0 + 1,
   
   [s](x0) = x0 + 2,
   
   [f](x0) = 2x0
  orientation:
   f(c(s(x),y)) = 8x + 8y + 16 >= 8x + 8y + 16 = f(c(x,s(y)))
   
   g(c(x,s(y))) = 4x + 4y + 9 >= 4x + 4y + 9 = g(c(s(x),y))
   
   g(s(f(x))) = 2x + 3 >= 2x + 1 = g(f(x))
  problem:
   f(c(s(x),y)) -> f(c(x,s(y)))
   g(c(x,s(y))) -> g(c(s(x),y))
  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=3
    
    interpretation:
                   [1 0 0]       
     [c](x0, x1) = [0 0 0]x0 + x1
                   [0 0 0]       ,
     
               [1 0 1]  
     [g](x0) = [0 1 0]x0
               [0 0 0]  ,
     
                    [0]
     [s](x0) = x0 + [0]
                    [1]
    orientation:
                    [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]                
     g(c(x,s(y))) = [0 0 0]x + [0 1 0]y + [0] >= [0 0 0]x + [0 1 0]y = g(c(s(x),y))
                    [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
    problem:
     
    Qed