YES
O(n^5)
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
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [g]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [0]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 0][X4]   [1]
       [X3]    [0 0 0 0 0][X3]   [0]
   [b]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [1]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 0 0 0 0][X4]   [0]
       [X3]    [0 0 0 0 0][X3]   [0]
   [a]([X2]) = [0 0 0 0 0][X2] + [0]
       [X1]    [0 0 0 0 0][X1]   [1]
       [X0]    [0 0 0 0 0][X0]   [0]
   
       [X4]    [1 1 1 1 0][X4]   [1]
       [X3]    [0 0 0 0 0][X3]   [1]
   [f]([X2]) = [0 0 0 0 1][X2] + [1]
       [X1]    [0 0 0 0 0][X1]   [1]
       [X0]    [0 0 0 0 1][X0]   [0]
   
   
   Qed