YES

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

Proof:
 Matrix Interpretation Processor:
  dimension: 1
  interpretation:
   [s](x0) = 4x0,
   
   [h](x0, x1) = x0 + 3x1 + 6,
   
   [f](x0) = 4x0 + 6,
   
   [g](x0) = 4x0 + 3
  orientation:
   f(g(x)) = 16x + 18 >= 16x + 18 = h(g(x),g(x))
   
   f(s(x)) = 16x + 6 >= 16x + 6 = h(s(x),s(x))
   
   g(x) = 4x + 3 >= 4x = s(x)
  problem:
   f(g(x)) -> h(g(x),g(x))
   f(s(x)) -> h(s(x),s(x))
  Matrix Interpretation Processor:
   dimension: 1
   interpretation:
    [s](x0) = 7x0,
    
    [h](x0, x1) = x0 + 2x1,
    
    [f](x0) = 4x0 + 1,
    
    [g](x0) = 4x0
   orientation:
    f(g(x)) = 16x + 1 >= 12x = h(g(x),g(x))
    
    f(s(x)) = 28x + 1 >= 21x = h(s(x),s(x))
   problem:
    
   Qed