YES

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

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [0] = 4,
   
   [g](x0, x1) = 4x0 + x1,
   
   [f](x0, x1) = 4x0 + x1 + 5,
   
   [s](x0) = 2x0
  orientation:
   f(s(x),y) = 8x + y + 5 >= 8x + y + 5 = f(x,g(x,y))
   
   f(0(),y) = y + 21 >= y = y
   
   g(x,y) = 4x + y >= y = y
  problem:
   f(s(x),y) -> f(x,g(x,y))
   g(x,y) -> y
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0, x1) = x0 + x1 + 1,
    
    [f](x0, x1) = x0 + x1 + 7,
    
    [s](x0) = 2x0 + 1
   orientation:
    f(s(x),y) = 2x + y + 8 >= 2x + y + 8 = f(x,g(x,y))
    
    g(x,y) = x + y + 1 >= y = y
   problem:
    f(s(x),y) -> f(x,g(x,y))
   Matrix Interpretation Processor: dim=1
    
    interpretation:
     [g](x0, x1) = x0 + x1 + 3,
     
     [f](x0, x1) = x0 + x1 + 1,
     
     [s](x0) = 2x0 + 6
    orientation:
     f(s(x),y) = 2x + y + 7 >= 2x + y + 4 = f(x,g(x,y))
    problem:
     
    Qed