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