YES

Problem:
 g(0()) -> 0()
 g(s(x)) -> f(g(x))
 f(0()) -> 0()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [f](x0) = x0 + 3,
   
   [s](x0) = x0 + 3,
   
   [g](x0) = x0,
   
   [0] = 4
  orientation:
   g(0()) = 4 >= 4 = 0()
   
   g(s(x)) = x + 3 >= x + 3 = f(g(x))
   
   f(0()) = 7 >= 4 = 0()
  problem:
   g(0()) -> 0()
   g(s(x)) -> f(g(x))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [f](x0) = x0,
    
    [s](x0) = x0 + 3,
    
    [g](x0) = x0,
    
    [0] = 6
   orientation:
    g(0()) = 6 >= 6 = 0()
    
    g(s(x)) = x + 3 >= x = f(g(x))
   problem:
    g(0()) -> 0()
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 0]     [1]
     [g](x0) = [0 0 0]x0 + [0]
               [0 0 0]     [0],
     
           [0]
     [0] = [0]
           [0]
    orientation:
              [1]    [0]      
     g(0()) = [0] >= [0] = 0()
              [0]    [0]      
    problem:
     
    Qed