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
   
   usable rules:
    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()
   interpretation:
    [g#](x0, x1) = 2x1,
    
    [f#](x0, x1) = x0 + x1,
    
    [s#](x0) = x0,
    
    [g](x0, x1) = 3x0 + 2x1 + 5/2,
    
    [f](x0, x1) = x0 + x1 + 1/2,
    
    [s](x0) = x0,
    
    [a] = 1
   orientation:
    s#(f(x,y)) = x + y + 1/2 >= x = s#(x)
    
    s#(f(x,y)) = x + y + 1/2 >= y = s#(y)
    
    s#(f(x,y)) = x + y + 1/2 >= x + y = f#(s(y),s(x))
    
    s#(g(x,y)) = 3x + 2y + 5/2 >= y = s#(y)
    
    s#(g(x,y)) = 3x + 2y + 5/2 >= x = s#(x)
    
    s#(g(x,y)) = 3x + 2y + 5/2 >= 2y = g#(s(x),s(y))
    
    f#(g(x,y),g(u,v)) = 3u + 2v + 3x + 2y + 5 >= v + y = f#(y,v)
    
    f#(g(x,y),g(u,v)) = 3u + 2v + 3x + 2y + 5 >= u + x = f#(x,u)
    
    f#(g(x,y),g(u,v)) = 3u + 2v + 3x + 2y + 5 >= 2v + 2y + 1 = g#(f(x,u),f(y,v))
    
    s(a()) = 1 >= 1 = a()
    
    s(s(x)) = x >= x = x
    
    s(f(x,y)) = x + y + 1/2 >= x + y + 1/2 = f(s(y),s(x))
    
    s(g(x,y)) = 3x + 2y + 5/2 >= 3x + 2y + 5/2 = g(s(x),s(y))
    
    f(x,a()) = x + 3/2 >= x = x
    
    f(a(),y) = y + 3/2 >= y = y
    
    f(g(x,y),g(u,v)) = 3u + 2v + 3x + 2y + 11/2 >= 3u + 2v + 3x + 2y + 5 = g(f(x,u),f(y,v))
    
    g(a(),a()) = 15/2 >= 1 = 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