YES
O(n^4)
TRS:
 {  f(x) -> g(x),
  f(a()) -> f(b()),
  g(b()) -> g(a())}
 DUP: We consider a non-duplicating system.
  Trs:
   {  f(x) -> g(x),
    f(a()) -> f(b()),
    g(b()) -> g(a())}
  Matrix Interpretation:
   Interpretation class: triangular
       [X3]    [1 0 0 1][X3]   [0]
       [X2]    [0 0 0 0][X2]   [0]
   [g]([X1]) = [0 0 0 1][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
         [0]
         [1]
   [a] = [1]
         [0]
   
         [0]
         [0]
   [b] = [0]
         [1]
   
       [X3]    [1 1 1 1][X3]   [1]
       [X2]    [0 1 1 0][X2]   [0]
   [f]([X1]) = [0 0 1 1][X1] + [0]
       [X0]    [0 0 0 0][X0]   [0]
   
   
   Qed