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)
  Matrix Interpretation Processor: dim=2
   
   interpretation:
    [g#](x0) = [0 1]x0 + [1],
    
    [mark#](x0) = [2 0]x0 + [2],
    
    [h#](x0) = [0 1]x0,
    
    [active#](x0) = [2 0]x0 + [1],
    
          [0]
    [d] = [2],
    
          [2]
    [c] = [0],
    
                 [2 0]     [0]
    [mark](x0) = [2 1]x0 + [1],
    
              [0 1]  
    [h](x0) = [1 0]x0,
    
                   [2 0]     [0]
    [active](x0) = [2 1]x0 + [1],
    
              [0 1]     [1]
    [g](x0) = [1 0]x0 + [0]
   orientation:
    active#(g(X)) = [0 2]X + [3] >= [0 1]X = h#(X)
    
    active#(g(X)) = [0 2]X + [3] >= [0 2]X + [2] = mark#(h(X))
    
    active#(c()) = 5 >= 2 = mark#(d())
    
    active#(h(d())) = 5 >= 1 = g#(c())
    
    active#(h(d())) = 5 >= 4 = mark#(g(c()))
    
    mark#(g(X)) = [0 2]X + [4] >= [0 2]X + [3] = active#(g(X))
    
    mark#(h(X)) = [0 2]X + [2] >= [0 2]X + [1] = active#(h(X))
    
    mark#(c()) = 6 >= 5 = active#(c())
    
    mark#(d()) = 2 >= 1 = active#(d())
    
    g#(mark(X)) = [2 1]X + [2] >= [0 1]X + [1] = g#(X)
    
    g#(active(X)) = [2 1]X + [2] >= [0 1]X + [1] = g#(X)
    
    h#(mark(X)) = [2 1]X + [1] >= [0 1]X = h#(X)
    
    h#(active(X)) = [2 1]X + [1] >= [0 1]X = h#(X)
    
                   [0 2]    [2]    [0 2]    [0]             
    active(g(X)) = [1 2]X + [3] >= [1 2]X + [1] = mark(h(X))
    
                  [4]    [0]            
    active(c()) = [5] >= [3] = mark(d())
    
                     [4]    [2]               
    active(h(d())) = [5] >= [5] = mark(g(c()))
    
                 [0 2]    [2]    [0 2]    [2]               
    mark(g(X)) = [1 2]X + [3] >= [1 2]X + [3] = active(g(X))
    
                 [0 2]    [0]    [0 2]    [0]               
    mark(h(X)) = [1 2]X + [1] >= [1 2]X + [1] = active(h(X))
    
                [4]    [4]              
    mark(c()) = [5] >= [5] = active(c())
    
                [0]    [0]              
    mark(d()) = [3] >= [3] = active(d())
    
                 [2 1]    [2]    [0 1]    [1]       
    g(mark(X)) = [2 0]X + [0] >= [1 0]X + [0] = g(X)
    
                   [2 1]    [2]    [0 1]    [1]       
    g(active(X)) = [2 0]X + [0] >= [1 0]X + [0] = g(X)
    
                 [2 1]    [1]    [0 1]        
    h(mark(X)) = [2 0]X + [0] >= [1 0]X = h(X)
    
                   [2 1]    [1]    [0 1]        
    h(active(X)) = [2 0]X + [0] >= [1 0]X = 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