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