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