YES

Problem:
 active(g(X)) -> mark(h(X))
 active(c()) -> mark(d())
 active(h(d())) -> mark(g(c()))
 mark(g(X)) -> active(g(X))
 mark(h(X)) -> active(h(X))
 mark(c()) -> active(c())
 mark(d()) -> active(d())
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)
 h(mark(X)) -> h(X)
 h(active(X)) -> h(X)

Proof:
 DP Processor:
  DPs:
   active#(g(X)) -> h#(X)
   active#(g(X)) -> mark#(h(X))
   active#(c()) -> mark#(d())
   active#(h(d())) -> g#(c())
   active#(h(d())) -> mark#(g(c()))
   mark#(g(X)) -> active#(g(X))
   mark#(h(X)) -> active#(h(X))
   mark#(c()) -> active#(c())
   mark#(d()) -> active#(d())
   g#(mark(X)) -> g#(X)
   g#(active(X)) -> g#(X)
   h#(mark(X)) -> h#(X)
   h#(active(X)) -> h#(X)
  TRS:
   active(g(X)) -> mark(h(X))
   active(c()) -> mark(d())
   active(h(d())) -> mark(g(c()))
   mark(g(X)) -> active(g(X))
   mark(h(X)) -> active(h(X))
   mark(c()) -> active(c())
   mark(d()) -> active(d())
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
   h(mark(X)) -> h(X)
   h(active(X)) -> h(X)
  Usable Rule Processor:
   DPs:
    active#(g(X)) -> h#(X)
    active#(g(X)) -> mark#(h(X))
    active#(c()) -> mark#(d())
    active#(h(d())) -> g#(c())
    active#(h(d())) -> mark#(g(c()))
    mark#(g(X)) -> active#(g(X))
    mark#(h(X)) -> active#(h(X))
    mark#(c()) -> active#(c())
    mark#(d()) -> active#(d())
    g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X)
    h#(mark(X)) -> h#(X)
    h#(active(X)) -> h#(X)
   TRS:
    h(mark(X)) -> h(X)
    h(active(X)) -> h(X)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   Matrix Interpretation Processor: dim=2
    
    usable rules:
     h(mark(X)) -> h(X)
     h(active(X)) -> h(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    interpretation:
     [g#](x0) = [1 0]x0,
     
     [mark#](x0) = [1 2]x0,
     
     [h#](x0) = [2 0]x0,
     
     [active#](x0) = [0 2]x0,
     
           [3]
     [d] = [0],
     
           [1]
     [c] = [2],
     
                  [2 0]     [3]
     [mark](x0) = [0 0]x0 + [0],
     
               [0 0]     [1]
     [h](x0) = [1 0]x0 + [0],
     
                    [2 0]     [3]
     [active](x0) = [0 0]x0 + [0],
     
               [0 0]     [1]
     [g](x0) = [1 0]x0 + [1]
    orientation:
     active#(g(X)) = [2 0]X + [2] >= [2 0]X = h#(X)
     
     active#(g(X)) = [2 0]X + [2] >= [2 0]X + [1] = mark#(h(X))
     
     active#(c()) = 4 >= 3 = mark#(d())
     
     active#(h(d())) = 6 >= 1 = g#(c())
     
     active#(h(d())) = 6 >= 5 = mark#(g(c()))
     
     mark#(g(X)) = [2 0]X + [3] >= [2 0]X + [2] = active#(g(X))
     
     mark#(h(X)) = [2 0]X + [1] >= [2 0]X = active#(h(X))
     
     mark#(c()) = 5 >= 4 = active#(c())
     
     mark#(d()) = 3 >= 0 = active#(d())
     
     g#(mark(X)) = [2 0]X + [3] >= [1 0]X = g#(X)
     
     g#(active(X)) = [2 0]X + [3] >= [1 0]X = g#(X)
     
     h#(mark(X)) = [4 0]X + [6] >= [2 0]X = h#(X)
     
     h#(active(X)) = [4 0]X + [6] >= [2 0]X = h#(X)
     
                  [0 0]    [1]    [0 0]    [1]       
     h(mark(X)) = [2 0]X + [3] >= [1 0]X + [0] = h(X)
     
                    [0 0]    [1]    [0 0]    [1]       
     h(active(X)) = [2 0]X + [3] >= [1 0]X + [0] = h(X)
     
                  [0 0]    [1]    [0 0]    [1]       
     g(mark(X)) = [2 0]X + [4] >= [1 0]X + [1] = g(X)
     
                    [0 0]    [1]    [0 0]    [1]       
     g(active(X)) = [2 0]X + [4] >= [1 0]X + [1] = g(X)
    problem:
     DPs:
      
     TRS:
      h(mark(X)) -> h(X)
      h(active(X)) -> h(X)
      g(mark(X)) -> g(X)
      g(active(X)) -> g(X)
    Qed