YES(?,O(n^2))
TRS:
 {
            f(x, a()) -> x,
  f(g(x, y), g(u, v)) -> g(f(x, u), f(y, v)),
            f(a(), y) -> y,
          g(a(), a()) -> a(),
            s f(x, y) -> f(s y, s x),
            s g(x, y) -> g(s x, s y),
                s a() -> a(),
                s s x -> x
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
              f(x, a()) -> x,
    f(g(x, y), g(u, v)) -> g(f(x, u), f(y, v)),
              f(a(), y) -> y,
            g(a(), a()) -> a(),
              s f(x, y) -> f(s y, s x),
              s g(x, y) -> g(s x, s y),
                  s a() -> a(),
                  s s x -> x
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 2][X1]   [3]
   [s]([X0]) = [0 1][X0] + [0]
   
         [2]
   [a] = [0]
   
       [X3]  [X1]    [1 0][X3]   [1 0][X1]   [0]
   [g]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [3]
   
       [X3]  [X1]    [1 3][X3]   [1 3][X1]   [0]
   [f]([X2], [X0]) = [0 1][X2] + [0 1][X0] + [3]
   
   
   Qed