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:
 DP Processor:
  DPs:
   s#(f(x,y)) -> s#(x)
   s#(f(x,y)) -> s#(y)
   s#(f(x,y)) -> f#(s(y),s(x))
   s#(g(x,y)) -> s#(y)
   s#(g(x,y)) -> s#(x)
   s#(g(x,y)) -> g#(s(x),s(y))
   f#(g(x,y),g(u,v)) -> f#(y,v)
   f#(g(x,y),g(u,v)) -> f#(x,u)
   f#(g(x,y),g(u,v)) -> g#(f(x,u),f(y,v))
  TRS:
   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()
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [g#](x0, x1) = x0 + 4,
    
    [f#](x0, x1) = 4x0 + 5x1,
    
    [s#](x0) = 5x0 + 6,
    
    [g](x0, x1) = 3x0 + x1 + 2,
    
    [f](x0, x1) = 6x0 + 6x1 + 5,
    
    [s](x0) = 4x0,
    
    [a] = 3
   orientation:
    s#(f(x,y)) = 30x + 30y + 31 >= 5x + 6 = s#(x)
    
    s#(f(x,y)) = 30x + 30y + 31 >= 5y + 6 = s#(y)
    
    s#(f(x,y)) = 30x + 30y + 31 >= 20x + 16y = f#(s(y),s(x))
    
    s#(g(x,y)) = 15x + 5y + 16 >= 5y + 6 = s#(y)
    
    s#(g(x,y)) = 15x + 5y + 16 >= 5x + 6 = s#(x)
    
    s#(g(x,y)) = 15x + 5y + 16 >= 4x + 4 = g#(s(x),s(y))
    
    f#(g(x,y),g(u,v)) = 15u + 5v + 12x + 4y + 18 >= 5v + 4y = f#(y,v)
    
    f#(g(x,y),g(u,v)) = 15u + 5v + 12x + 4y + 18 >= 5u + 4x = f#(x,u)
    
    f#(g(x,y),g(u,v)) = 15u + 5v + 12x + 4y + 18 >= 6u + 6x + 9 = g#(f(x,u),f(y,v))
    
    s(a()) = 12 >= 3 = a()
    
    s(s(x)) = 16x >= x = x
    
    s(f(x,y)) = 24x + 24y + 20 >= 24x + 24y + 5 = f(s(y),s(x))
    
    s(g(x,y)) = 12x + 4y + 8 >= 12x + 4y + 2 = g(s(x),s(y))
    
    f(x,a()) = 6x + 23 >= x = x
    
    f(a(),y) = 6y + 23 >= y = y
    
    f(g(x,y),g(u,v)) = 18u + 6v + 18x + 6y + 29 >= 18u + 6v + 18x + 6y + 22 = g(f(x,u),f(y,v))
    
    g(a(),a()) = 14 >= 3 = a()
   problem:
    DPs:
     
    TRS:
     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()
   Qed