YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f'](x0, x1, x2) = 7x0 + x1 + 6x2 + 1,
   
   [s](x0) = x0 + 2,
   
   [h](x0) = x0,
   
   [f](x0) = x0,
   
   [g](x0) = x0
  orientation:
   f(g(x)) = x >= x = g(f(f(x)))
   
   f(h(x)) = x >= x = h(g(x))
   
   f'(s(x),y,y) = 7x + 7y + 15 >= 7x + 7y + 13 = f'(y,x,s(x))
  problem:
   f(g(x)) -> g(f(f(x)))
   f(h(x)) -> h(g(x))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
              [1 0 0]     [0]
    [h](x0) = [0 0 0]x0 + [1]
              [0 0 0]     [1],
    
              [1 1 0]  
    [f](x0) = [0 0 1]x0
              [0 1 0]  ,
    
              [1 0 0]     [0]
    [g](x0) = [0 1 1]x0 + [1]
              [0 1 1]     [1]
   orientation:
              [1 1 1]    [1]    [1 1 1]    [0]             
    f(g(x)) = [0 1 1]x + [1] >= [0 1 1]x + [1] = g(f(f(x)))
              [0 1 1]    [1]    [0 1 1]    [1]             
    
              [1 0 0]    [1]    [1 0 0]    [0]          
    f(h(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = h(g(x))
              [0 0 0]    [1]    [0 0 0]    [1]          
   problem:
    
   Qed