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:
   [g](x0, x1) = x0 + 4x1 + 1,
   
   [f](x0, x1) = 2x0 + 2x1,
   
   [s](x0) = x0,
   
   [a] = 6
  orientation:
   s(a()) = 6 >= 6 = a()
   
   s(s(x)) = x >= x = x
   
   s(f(x,y)) = 2x + 2y >= 2x + 2y = f(s(y),s(x))
   
   s(g(x,y)) = x + 4y + 1 >= x + 4y + 1 = g(s(x),s(y))
   
   f(x,a()) = 2x + 12 >= x = x
   
   f(a(),y) = 2y + 12 >= y = y
   
   f(g(x,y),g(u,v)) = 2u + 8v + 2x + 8y + 4 >= 2u + 8v + 2x + 8y + 1 = g(f(x,u),f(y,v))
   
   g(a(),a()) = 31 >= 6 = a()
  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))
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g](x0, x1) = 2x0 + 2x1 + 4,
    
    [f](x0, x1) = 4x0 + 4x1 + 2,
    
    [s](x0) = 5x0,
    
    [a] = 0
   orientation:
    s(a()) = 0 >= 0 = a()
    
    s(s(x)) = 25x >= x = x
    
    s(f(x,y)) = 20x + 20y + 10 >= 20x + 20y + 2 = f(s(y),s(x))
    
    s(g(x,y)) = 10x + 10y + 20 >= 10x + 10y + 4 = g(s(x),s(y))
   problem:
    s(a()) -> a()
    s(s(x)) -> x
   Matrix Interpretation Processor: dim=3
    
    interpretation:
               [1 0 1]  
     [s](x0) = [0 0 1]x0
               [0 1 0]  ,
     
           [0]
     [a] = [1]
           [1]
    orientation:
              [1]    [0]      
     s(a()) = [1] >= [1] = a()
              [1]    [1]      
     
               [1 1 1]          
     s(s(x)) = [0 1 0]x >= x = x
               [0 0 1]          
    problem:
     s(s(x)) -> x
    Matrix Interpretation Processor: dim=3
     
     interpretation:
                [1 1 0]     [0]
      [s](x0) = [0 0 1]x0 + [1]
                [0 1 0]     [0]
     orientation:
                [1 1 1]    [1]         
      s(s(x)) = [0 1 0]x + [1] >= x = x
                [0 0 1]    [1]         
     problem:
      
     Qed