YES

Problem:
 active(f(X)) -> mark(g(h(f(X))))
 active(f(X)) -> f(active(X))
 active(h(X)) -> h(active(X))
 f(mark(X)) -> mark(f(X))
 h(mark(X)) -> mark(h(X))
 proper(f(X)) -> f(proper(X))
 proper(g(X)) -> g(proper(X))
 proper(h(X)) -> h(proper(X))
 f(ok(X)) -> ok(f(X))
 g(ok(X)) -> ok(g(X))
 h(ok(X)) -> ok(h(X))
 top(mark(X)) -> top(proper(X))
 top(ok(X)) -> top(active(X))

Proof:
 DP Processor:
  DPs:
   active#(f(X)) -> h#(f(X))
   active#(f(X)) -> g#(h(f(X)))
   active#(f(X)) -> active#(X)
   active#(f(X)) -> f#(active(X))
   active#(h(X)) -> active#(X)
   active#(h(X)) -> h#(active(X))
   f#(mark(X)) -> f#(X)
   h#(mark(X)) -> h#(X)
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   proper#(h(X)) -> proper#(X)
   proper#(h(X)) -> h#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(X)
   h#(ok(X)) -> h#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(f(X)) -> mark(g(h(f(X))))
   active(f(X)) -> f(active(X))
   active(h(X)) -> h(active(X))
   f(mark(X)) -> mark(f(X))
   h(mark(X)) -> mark(h(X))
   proper(f(X)) -> f(proper(X))
   proper(g(X)) -> g(proper(X))
   proper(h(X)) -> h(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   h(ok(X)) -> ok(h(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Usable Rule Processor:
   DPs:
    active#(f(X)) -> h#(f(X))
    active#(f(X)) -> g#(h(f(X)))
    active#(f(X)) -> active#(X)
    active#(f(X)) -> f#(active(X))
    active#(h(X)) -> active#(X)
    active#(h(X)) -> h#(active(X))
    f#(mark(X)) -> f#(X)
    h#(mark(X)) -> h#(X)
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    proper#(h(X)) -> proper#(X)
    proper#(h(X)) -> h#(proper(X))
    f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X)
    h#(ok(X)) -> h#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    f(mark(X)) -> mark(f(X))
    f(ok(X)) -> ok(f(X))
    h(mark(X)) -> mark(h(X))
    h(ok(X)) -> ok(h(X))
    active(f(X)) -> mark(g(h(f(X))))
    active(f(X)) -> f(active(X))
    active(h(X)) -> h(active(X))
    g(ok(X)) -> ok(g(X))
    proper(f(X)) -> f(proper(X))
    proper(g(X)) -> g(proper(X))
    proper(h(X)) -> h(proper(X))
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     f(mark(X)) -> mark(f(X))
     f(ok(X)) -> ok(f(X))
     h(mark(X)) -> mark(h(X))
     h(ok(X)) -> ok(h(X))
     active(f(X)) -> mark(g(h(f(X))))
     active(f(X)) -> f(active(X))
     active(h(X)) -> h(active(X))
     g(ok(X)) -> ok(g(X))
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     proper(h(X)) -> h(proper(X))
    interpretation:
     [top#](x0) = 4x0 + 3,
     
     [proper#](x0) = 3/2x0 + 1,
     
     [f#](x0) = 1/2x0 + 3/2,
     
     [g#](x0) = x0 + 1/2,
     
     [h#](x0) = 1/2x0 + 1,
     
     [active#](x0) = 2x0 + 13/2,
     
     [ok](x0) = 5x0 + 2,
     
     [proper](x0) = x0,
     
     [mark](x0) = x0 + 1/2,
     
     [g](x0) = 2x0 + 1/2,
     
     [h](x0) = 2x0 + 1/2,
     
     [active](x0) = 5x0 + 3/2,
     
     [f](x0) = 2x0 + 1/2
    orientation:
     active#(f(X)) = 4X + 15/2 >= X + 5/4 = h#(f(X))
     
     active#(f(X)) = 4X + 15/2 >= 4X + 2 = g#(h(f(X)))
     
     active#(f(X)) = 4X + 15/2 >= 2X + 13/2 = active#(X)
     
     active#(f(X)) = 4X + 15/2 >= 5/2X + 9/4 = f#(active(X))
     
     active#(h(X)) = 4X + 15/2 >= 2X + 13/2 = active#(X)
     
     active#(h(X)) = 4X + 15/2 >= 5/2X + 7/4 = h#(active(X))
     
     f#(mark(X)) = 1/2X + 7/4 >= 1/2X + 3/2 = f#(X)
     
     h#(mark(X)) = 1/2X + 5/4 >= 1/2X + 1 = h#(X)
     
     proper#(f(X)) = 3X + 7/4 >= 3/2X + 1 = proper#(X)
     
     proper#(f(X)) = 3X + 7/4 >= 1/2X + 3/2 = f#(proper(X))
     
     proper#(g(X)) = 3X + 7/4 >= 3/2X + 1 = proper#(X)
     
     proper#(g(X)) = 3X + 7/4 >= X + 1/2 = g#(proper(X))
     
     proper#(h(X)) = 3X + 7/4 >= 3/2X + 1 = proper#(X)
     
     proper#(h(X)) = 3X + 7/4 >= 1/2X + 1 = h#(proper(X))
     
     f#(ok(X)) = 5/2X + 5/2 >= 1/2X + 3/2 = f#(X)
     
     g#(ok(X)) = 5X + 5/2 >= X + 1/2 = g#(X)
     
     h#(ok(X)) = 5/2X + 2 >= 1/2X + 1 = h#(X)
     
     top#(mark(X)) = 4X + 5 >= 3/2X + 1 = proper#(X)
     
     top#(mark(X)) = 4X + 5 >= 4X + 3 = top#(proper(X))
     
     top#(ok(X)) = 20X + 11 >= 2X + 13/2 = active#(X)
     
     top#(ok(X)) = 20X + 11 >= 20X + 9 = top#(active(X))
     
     f(mark(X)) = 2X + 3/2 >= 2X + 1 = mark(f(X))
     
     f(ok(X)) = 10X + 9/2 >= 10X + 9/2 = ok(f(X))
     
     h(mark(X)) = 2X + 3/2 >= 2X + 1 = mark(h(X))
     
     h(ok(X)) = 10X + 9/2 >= 10X + 9/2 = ok(h(X))
     
     active(f(X)) = 10X + 4 >= 8X + 4 = mark(g(h(f(X))))
     
     active(f(X)) = 10X + 4 >= 10X + 7/2 = f(active(X))
     
     active(h(X)) = 10X + 4 >= 10X + 7/2 = h(active(X))
     
     g(ok(X)) = 10X + 9/2 >= 10X + 9/2 = ok(g(X))
     
     proper(f(X)) = 2X + 1/2 >= 2X + 1/2 = f(proper(X))
     
     proper(g(X)) = 2X + 1/2 >= 2X + 1/2 = g(proper(X))
     
     proper(h(X)) = 2X + 1/2 >= 2X + 1/2 = h(proper(X))
    problem:
     DPs:
      
     TRS:
      f(mark(X)) -> mark(f(X))
      f(ok(X)) -> ok(f(X))
      h(mark(X)) -> mark(h(X))
      h(ok(X)) -> ok(h(X))
      active(f(X)) -> mark(g(h(f(X))))
      active(f(X)) -> f(active(X))
      active(h(X)) -> h(active(X))
      g(ok(X)) -> ok(g(X))
      proper(f(X)) -> f(proper(X))
      proper(g(X)) -> g(proper(X))
      proper(h(X)) -> h(proper(X))
    Qed