YES

Problem:
 s(a()) -> a()
 s(s(x)) -> x
 s(f(x,y)) -> f(s(y),s(x))
 s(g(x,y)) -> g(s(x),s(y))
 f(x,a()) -> x
 f(a(),y) -> y
 f(g(x,y),g(u,v)) -> g(f(x,u),f(y,v))
 g(a(),a()) -> a()

Proof:
 Matrix Interpretation Processor: dim=1
  
  interpretation:
   [s](x0) = 4x0,
   
   [g](x0, x1) = 4x0 + 2x1 + 4,
   
   [a] = 0,
   
   [f](x0, x1) = x0 + x1
  orientation:
   s(a()) = 0 >= 0 = a()
   
   s(s(x)) = 16x >= x = x
   
   s(f(x,y)) = 4x + 4y >= 4x + 4y = f(s(y),s(x))
   
   s(g(x,y)) = 16x + 8y + 16 >= 16x + 8y + 4 = g(s(x),s(y))
   
   f(x,a()) = x >= x = x
   
   f(a(),y) = y >= y = y
   
   f(g(x,y),g(u,v)) = 4u + 2v + 4x + 2y + 8 >= 4u + 2v + 4x + 2y + 4 = g(f(x,u),f(y,v))
   
   g(a(),a()) = 4 >= 0 = a()
  problem:
   s(a()) -> a()
   s(s(x)) -> x
   s(f(x,y)) -> f(s(y),s(x))
   f(x,a()) -> x
   f(a(),y) -> y
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [s](x0) = 4x0 + 2,
    
    [a] = 2,
    
    [f](x0, x1) = 5x0 + 5x1 + 6
   orientation:
    s(a()) = 10 >= 2 = a()
    
    s(s(x)) = 16x + 10 >= x = x
    
    s(f(x,y)) = 20x + 20y + 26 >= 20x + 20y + 26 = f(s(y),s(x))
    
    f(x,a()) = 5x + 16 >= x = x
    
    f(a(),y) = 5y + 16 >= y = y
   problem:
    s(f(x,y)) -> f(s(y),s(x))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 1 1]  
     [s](x0) = [0 1 0]x0
               [1 0 1]  ,
     
                   [1 0 0]     [1 0 0]     [0]
     [f](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                   [0 1 1]     [0 1 1]     [0]
    orientation:
                 [1 1 1]    [1 1 1]    [1]    [1 1 1]    [1 1 1]    [0]               
     s(f(x,y)) = [0 0 0]x + [0 0 0]y + [1] >= [0 0 0]x + [0 0 0]y + [1] = f(s(y),s(x))
                 [1 1 1]    [1 1 1]    [0]    [1 1 1]    [1 1 1]    [0]               
    problem:
     
    Qed