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)
  TDG 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)
   graph:
    g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
    g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
    mark#(d()) -> active#(d()) -> active#(h(d())) -> mark#(g(c()))
    mark#(d()) -> active#(d()) -> active#(h(d())) -> g#(c())
    mark#(d()) -> active#(d()) -> active#(c()) -> mark#(d())
    mark#(d()) -> active#(d()) -> active#(g(X)) -> mark#(h(X))
    mark#(d()) -> active#(d()) -> active#(g(X)) -> h#(X)
    mark#(c()) -> active#(c()) -> active#(h(d())) -> mark#(g(c()))
    mark#(c()) -> active#(c()) -> active#(h(d())) -> g#(c())
    mark#(c()) -> active#(c()) -> active#(c()) -> mark#(d())
    mark#(c()) -> active#(c()) -> active#(g(X)) -> mark#(h(X))
    mark#(c()) -> active#(c()) -> active#(g(X)) -> h#(X)
    mark#(h(X)) -> active#(h(X)) -> active#(h(d())) -> mark#(g(c()))
    mark#(h(X)) -> active#(h(X)) -> active#(h(d())) -> g#(c())
    mark#(h(X)) -> active#(h(X)) -> active#(c()) -> mark#(d())
    mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> mark#(h(X))
    mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> h#(X)
    mark#(g(X)) -> active#(g(X)) -> active#(h(d())) -> mark#(g(c()))
    mark#(g(X)) -> active#(g(X)) -> active#(h(d())) -> g#(c())
    mark#(g(X)) -> active#(g(X)) -> active#(c()) -> mark#(d())
    mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> mark#(h(X))
    mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> h#(X)
    h#(mark(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    h#(mark(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
    h#(active(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    h#(active(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
    active#(c()) -> mark#(d()) -> mark#(d()) -> active#(d())
    active#(c()) -> mark#(d()) -> mark#(c()) -> active#(c())
    active#(c()) -> mark#(d()) -> mark#(h(X)) -> active#(h(X))
    active#(c()) -> mark#(d()) -> mark#(g(X)) -> active#(g(X))
    active#(h(d())) -> g#(c()) -> g#(active(X)) -> g#(X)
    active#(h(d())) -> g#(c()) -> g#(mark(X)) -> g#(X)
    active#(h(d())) -> mark#(g(c())) -> mark#(d()) -> active#(d())
    active#(h(d())) -> mark#(g(c())) -> mark#(c()) -> active#(c())
    active#(h(d())) -> mark#(g(c())) ->
    mark#(h(X)) -> active#(h(X))
    active#(h(d())) -> mark#(g(c())) -> mark#(g(X)) -> active#(g(X))
    active#(g(X)) -> mark#(h(X)) -> mark#(d()) -> active#(d())
    active#(g(X)) -> mark#(h(X)) -> mark#(c()) -> active#(c())
    active#(g(X)) -> mark#(h(X)) -> mark#(h(X)) -> active#(h(X))
    active#(g(X)) -> mark#(h(X)) -> mark#(g(X)) -> active#(g(X))
    active#(g(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    active#(g(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
   EDG 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)
    graph:
     g#(mark(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
     g#(mark(X)) -> g#(X) -> g#(active(X)) -> g#(X)
     g#(active(X)) -> g#(X) -> g#(mark(X)) -> g#(X)
     g#(active(X)) -> g#(X) -> g#(active(X)) -> g#(X)
     mark#(c()) -> active#(c()) -> active#(c()) -> mark#(d())
     mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> h#(X)
     mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> mark#(h(X))
     mark#(h(X)) -> active#(h(X)) -> active#(h(d())) -> g#(c())
     mark#(h(X)) -> active#(h(X)) -> active#(h(d())) -> mark#(g(c()))
     mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> h#(X)
     mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> mark#(h(X))
     mark#(g(X)) -> active#(g(X)) -> active#(h(d())) -> g#(c())
     mark#(g(X)) -> active#(g(X)) -> active#(h(d())) -> mark#(g(c()))
     h#(mark(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
     h#(mark(X)) -> h#(X) -> h#(active(X)) -> h#(X)
     h#(active(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
     h#(active(X)) -> h#(X) -> h#(active(X)) -> h#(X)
     active#(c()) -> mark#(d()) -> mark#(d()) -> active#(d())
     active#(h(d())) -> mark#(g(c())) -> mark#(g(X)) -> active#(g(X))
     active#(g(X)) -> mark#(h(X)) -> mark#(g(X)) -> active#(g(X))
     active#(g(X)) -> mark#(h(X)) -> mark#(h(X)) -> active#(h(X))
     active#(g(X)) -> h#(X) -> h#(mark(X)) -> h#(X)
     active#(g(X)) -> h#(X) -> h#(active(X)) -> h#(X)
    CDG 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)
     graph:
      mark#(c()) -> active#(c()) -> active#(c()) -> mark#(d())
      mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> mark#(h(X))
      mark#(h(X)) -> active#(h(X)) -> active#(g(X)) -> h#(X)
      mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> mark#(h(X))
      mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> h#(X)
      active#(c()) -> mark#(d()) -> mark#(d()) -> active#(d())
      active#(h(d())) -> mark#(g(c())) -> mark#(g(X)) -> active#(g(X))
      active#(g(X)) -> mark#(h(X)) -> mark#(h(X)) -> active#(h(X))
      active#(g(X)) -> mark#(h(X)) -> mark#(g(X)) -> active#(g(X))
     SCC Processor:
      #sccs: 1
      #rules: 3
      #arcs: 9/169
      DPs:
       mark#(h(X)) -> active#(h(X))
       active#(g(X)) -> mark#(h(X))
       mark#(g(X)) -> active#(g(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)
      Matrix Interpretation Processor: dim=1
       
       interpretation:
        [mark#](x0) = 2x0 + 7/2,
        
        [active#](x0) = x0 + 3,
        
        [d] = 0,
        
        [c] = 0,
        
        [mark](x0) = 0,
        
        [h](x0) = 0,
        
        [active](x0) = 0,
        
        [g](x0) = 1
       orientation:
        mark#(h(X)) = 7/2 >= 3 = active#(h(X))
        
        active#(g(X)) = 4 >= 7/2 = mark#(h(X))
        
        mark#(g(X)) = 11/2 >= 4 = active#(g(X))
        
        active(g(X)) = 0 >= 0 = mark(h(X))
        
        active(c()) = 0 >= 0 = mark(d())
        
        active(h(d())) = 0 >= 0 = mark(g(c()))
        
        mark(g(X)) = 0 >= 0 = active(g(X))
        
        mark(h(X)) = 0 >= 0 = active(h(X))
        
        mark(c()) = 0 >= 0 = active(c())
        
        mark(d()) = 0 >= 0 = active(d())
        
        g(mark(X)) = 1 >= 1 = g(X)
        
        g(active(X)) = 1 >= 1 = g(X)
        
        h(mark(X)) = 0 >= 0 = h(X)
        
        h(active(X)) = 0 >= 0 = h(X)
       problem:
        DPs:
         
        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)
       Qed