YES
O(n^3)
TRS:
 {   f(f(X)) -> f(a(b(f(X)))),
  f(a(g(X))) -> b(X),
        b(X) -> a(X)}
 DUP: We consider a non-duplicating system.
  Trs:
   {   f(f(X)) -> f(a(b(f(X)))),
    f(a(g(X))) -> b(X),
          b(X) -> a(X)}
  Matrix Interpretation:
   Interpretation class: triangular
       [X2]    [1 0 1][X2]   [1]
   [g]([X1]) = [0 0 0][X1] + [0]
       [X0]    [0 0 1][X0]   [1]
   
       [X2]    [1 0 0][X2]   [1]
   [b]([X1]) = [0 0 1][X1] + [0]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 0 0][X2]   [0]
   [a]([X1]) = [0 0 1][X1] + [0]
       [X0]    [0 0 0][X0]   [0]
   
       [X2]    [1 1 1][X2]   [0]
   [f]([X1]) = [0 1 0][X1] + [1]
       [X0]    [0 0 0][X0]   [1]
   
   
   Qed