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