YES

Problem:
 f(c(X,s(Y))) -> f(c(s(X),Y))
 g(c(s(X),Y)) -> f(c(X,s(Y)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
                 [1 0 0]     [1 0 1]  
   [c](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                 [0 0 0]     [0 1 0]  ,
   
             [1 0 0]     [1]
   [g](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [0],
   
             [1 0 0]     [0]
   [s](x0) = [0 0 1]x0 + [0]
             [0 0 1]     [1],
   
             [1 0 0]  
   [f](x0) = [0 0 0]x0
             [0 0 0]  
  orientation:
                  [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]                
   f(c(X,s(Y))) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y = f(c(s(X),Y))
                  [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
   
                  [1 0 0]    [1 0 1]    [1]    [1 0 0]    [1 0 1]    [1]               
   g(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]    [0]    [0 0 0]    [0 0 0]    [0]               
  problem:
   g(c(s(X),Y)) -> f(c(X,s(Y)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
                  [1 0 0]     [1 0 0]  
    [c](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                  [0 0 0]     [0 0 0]  ,
    
              [1 0 0]     [1]
    [g](x0) = [0 0 0]x0 + [0]
              [0 0 0]     [0],
    
              [1 0 0]  
    [s](x0) = [0 0 0]x0
              [0 0 0]  ,
    
              [1 0 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                   [1 0 0]    [1 0 0]    [1]    [1 0 0]    [1 0 0]                
    g(c(s(X),Y)) = [0 0 0]X + [0 0 0]Y + [0] >= [0 0 0]X + [0 0 0]Y = f(c(X,s(Y)))
                   [0 0 0]    [0 0 0]    [0]    [0 0 0]    [0 0 0]                
   problem:
    
   Qed