YES
O(n^2)
TRS:
 {
      g(ok(X)) -> ok(g(X)),
    h(mark(X)) -> mark(h(X)),
      h(ok(X)) -> ok(h(X)),
    f(mark(X)) -> mark(f(X)),
      f(ok(X)) -> ok(f(X)),
  active(h(X)) -> h(active(X)),
  active(f(X)) -> mark(g(h(f(X)))),
  active(f(X)) -> f(active(X)),
  proper(g(X)) -> g(proper(X)),
  proper(h(X)) -> h(proper(X)),
  proper(f(X)) -> f(proper(X)),
  top(mark(X)) -> top(proper(X)),
    top(ok(X)) -> top(active(X))
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
        g(ok(X)) -> ok(g(X)),
      h(mark(X)) -> mark(h(X)),
        h(ok(X)) -> ok(h(X)),
      f(mark(X)) -> mark(f(X)),
        f(ok(X)) -> ok(f(X)),
    active(h(X)) -> h(active(X)),
    active(f(X)) -> mark(g(h(f(X)))),
    active(f(X)) -> f(active(X)),
    proper(g(X)) -> g(proper(X)),
    proper(h(X)) -> h(proper(X)),
    proper(f(X)) -> f(proper(X)),
    top(mark(X)) -> top(proper(X)),
      top(ok(X)) -> top(active(X))
   }
  Matrix Interpretation:
   Interpretation class: triangular
         [X1]    [1 1][X1]   [0]
   [top]([X0]) = [0 1][X0] + [0]
   
        [X1]    [1 6][X1]   [0]
   [ok]([X0]) = [0 1][X0] + [7]
   
            [X1]    [1 1][X1]   [0]
   [proper]([X0]) = [0 1][X0] + [0]
   
            [X1]    [1 6][X1]   [0]
   [active]([X0]) = [0 1][X0] + [5]
   
       [X1]    [1 6][X1]   [0]
   [f]([X0]) = [0 1][X0] + [6]
   
       [X1]    [1 1][X1]   [0]
   [h]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 1][X1]   [0]
   [g]([X0]) = [0 1][X0] + [1]
   
          [X1]    [1 2][X1]   [0]
   [mark]([X0]) = [0 1][X0] + [3]
   
   
   Qed