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)
   SCC Processor:
    #sccs: 3
    #rules: 11
    #arcs: 44/169
    DPs:
     mark#(d()) -> active#(d())
     active#(g(X)) -> mark#(h(X))
     mark#(g(X)) -> active#(g(X))
     active#(c()) -> mark#(d())
     mark#(h(X)) -> active#(h(X))
     active#(h(d())) -> mark#(g(c()))
     mark#(c()) -> active#(c())
    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)
    EDG Processor:
     DPs:
      mark#(d()) -> active#(d())
      active#(g(X)) -> mark#(h(X))
      mark#(g(X)) -> active#(g(X))
      active#(c()) -> mark#(d())
      mark#(h(X)) -> active#(h(X))
      active#(h(d())) -> mark#(g(c()))
      mark#(c()) -> active#(c())
     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#(h(d())) -> mark#(g(c()))
      mark#(g(X)) -> active#(g(X)) -> active#(g(X)) -> mark#(h(X))
      mark#(g(X)) -> active#(g(X)) -> active#(h(d())) -> mark#(g(c()))
      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))
     CDG Processor:
      DPs:
       mark#(d()) -> active#(d())
       active#(g(X)) -> mark#(h(X))
       mark#(g(X)) -> active#(g(X))
       active#(c()) -> mark#(d())
       mark#(h(X)) -> active#(h(X))
       active#(h(d())) -> mark#(g(c()))
       mark#(c()) -> active#(c())
      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#(g(X)) -> active#(g(X)) -> active#(g(X)) -> mark#(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: 7/49
       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)
       Arctic Interpretation Processor:
        dimension: 1
        interpretation:
         [mark#](x0) = 4,
         
         [active#](x0) = x0 + 0,
         
         [d] = 0,
         
         [c] = 3,
         
         [mark](x0) = 0,
         
         [h](x0) = 2,
         
         [active](x0) = 0,
         
         [g](x0) = 4
        orientation:
         mark#(h(X)) = 4 >= 2 = active#(h(X))
         
         active#(g(X)) = 4 >= 4 = mark#(h(X))
         
         mark#(g(X)) = 4 >= 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)) = 4 >= 4 = g(X)
         
         g(active(X)) = 4 >= 4 = g(X)
         
         h(mark(X)) = 2 >= 2 = h(X)
         
         h(active(X)) = 2 >= 2 = h(X)
        problem:
         DPs:
          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)
        Arctic Interpretation Processor:
         dimension: 1
         interpretation:
          [mark#](x0) = 1x0,
          
          [active#](x0) = x0,
          
          [d] = 1,
          
          [c] = 0,
          
          [mark](x0) = x0 + 1,
          
          [h](x0) = 3x0,
          
          [active](x0) = x0 + 1,
          
          [g](x0) = 4x0
         orientation:
          active#(g(X)) = 4X >= 4X = mark#(h(X))
          
          mark#(g(X)) = 5X >= 4X = active#(g(X))
          
          active(g(X)) = 4X + 1 >= 3X + 1 = mark(h(X))
          
          active(c()) = 1 >= 1 = mark(d())
          
          active(h(d())) = 4 >= 4 = mark(g(c()))
          
          mark(g(X)) = 4X + 1 >= 4X + 1 = active(g(X))
          
          mark(h(X)) = 3X + 1 >= 3X + 1 = active(h(X))
          
          mark(c()) = 1 >= 1 = active(c())
          
          mark(d()) = 1 >= 1 = active(d())
          
          g(mark(X)) = 4X + 5 >= 4X = g(X)
          
          g(active(X)) = 4X + 5 >= 4X = g(X)
          
          h(mark(X)) = 3X + 4 >= 3X = h(X)
          
          h(active(X)) = 3X + 4 >= 3X = h(X)
         problem:
          DPs:
           active#(g(X)) -> mark#(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)
         SCC Processor:
          #sccs: 0
          #rules: 0
          #arcs: 4/1
          
    
    DPs:
     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)
    Subterm Criterion Processor:
     simple projection:
      pi(h#) = 0
     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
    
    DPs:
     g#(mark(X)) -> g#(X)
     g#(active(X)) -> 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)
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     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