YES(?,O(n^3))
TRS:
 {
              f X -> n__f X,
    f n__f n__a() -> f n__g n__f n__a(),
              g X -> n__g X,
              a() -> n__a(),
       activate X -> X,
  activate n__g X -> g activate X,
  activate n__f X -> f X,
  activate n__a() -> a()
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
                f X -> n__f X,
      f n__f n__a() -> f n__g n__f n__a(),
                g X -> n__g X,
                a() -> n__a(),
         activate X -> X,
    activate n__g X -> g activate X,
    activate n__f X -> f X,
    activate n__a() -> a()
   }
  Matrix Interpretation:
   Interpretation class: triangular
              [X2]    [1 0 1][X2]   [2]
   [activate]([X1]) = [0 1 0][X1] + [0]
              [X0]    [0 0 1][X0]   [1]
   
         [3]
   [a] = [3]
         [2]
   
            [2]
   [n__a] = [3]
            [2]
   
          [X2]    [1 1 0][X2]   [2]
   [n__f]([X1]) = [0 1 3][X1] + [0]
          [X0]    [0 0 0][X0]   [0]
   
          [X2]    [1 0 1][X2]   [2]
   [n__g]([X1]) = [0 0 0][X1] + [0]
          [X0]    [0 0 1][X0]   [3]
   
       [X2]    [1 0 1][X2]   [3]
   [g]([X1]) = [0 0 0][X1] + [0]
       [X0]    [0 0 1][X0]   [3]
   
       [X2]    [1 1 0][X2]   [3]
   [f]([X1]) = [0 1 3][X1] + [0]
       [X0]    [0 0 0][X0]   [0]
   
   
   Qed