YES

Problem:
 active(c()) -> mark(f(g(c())))
 active(f(g(X))) -> mark(g(X))
 mark(c()) -> active(c())
 mark(f(X)) -> active(f(X))
 mark(g(X)) -> active(g(X))
 f(mark(X)) -> f(X)
 f(active(X)) -> f(X)
 g(mark(X)) -> g(X)
 g(active(X)) -> g(X)

Proof:
 DP Processor:
  DPs:
   active#(c()) -> g#(c())
   active#(c()) -> f#(g(c()))
   active#(c()) -> mark#(f(g(c())))
   active#(f(g(X))) -> mark#(g(X))
   mark#(c()) -> active#(c())
   mark#(f(X)) -> active#(f(X))
   mark#(g(X)) -> active#(g(X))
   f#(mark(X)) -> f#(X)
   f#(active(X)) -> f#(X)
   g#(mark(X)) -> g#(X)
   g#(active(X)) -> g#(X)
  TRS:
   active(c()) -> mark(f(g(c())))
   active(f(g(X))) -> mark(g(X))
   mark(c()) -> active(c())
   mark(f(X)) -> active(f(X))
   mark(g(X)) -> active(g(X))
   f(mark(X)) -> f(X)
   f(active(X)) -> f(X)
   g(mark(X)) -> g(X)
   g(active(X)) -> g(X)
  CDG Processor:
   DPs:
    active#(c()) -> g#(c())
    active#(c()) -> f#(g(c()))
    active#(c()) -> mark#(f(g(c())))
    active#(f(g(X))) -> mark#(g(X))
    mark#(c()) -> active#(c())
    mark#(f(X)) -> active#(f(X))
    mark#(g(X)) -> active#(g(X))
    f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X)
    g#(mark(X)) -> g#(X)
    g#(active(X)) -> g#(X)
   TRS:
    active(c()) -> mark(f(g(c())))
    active(f(g(X))) -> mark(g(X))
    mark(c()) -> active(c())
    mark(f(X)) -> active(f(X))
    mark(g(X)) -> active(g(X))
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
   graph:
    mark#(f(X)) -> active#(f(X)) -> active#(f(g(X))) -> mark#(g(X))
    mark#(c()) -> active#(c()) -> active#(c()) -> g#(c())
    mark#(c()) -> active#(c()) -> active#(c()) -> f#(g(c()))
    mark#(c()) -> active#(c()) -> active#(c()) -> mark#(f(g(c())))
    f#(mark(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(mark(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(mark(X)) -> f#(X)
    f#(active(X)) -> f#(X) -> f#(active(X)) -> f#(X)
    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)
    active#(f(g(X))) -> mark#(g(X)) -> mark#(g(X)) -> active#(g(X))
    active#(c()) -> mark#(f(g(c()))) -> mark#(f(X)) -> active#(f(X))
   SCC Processor:
    #sccs: 2
    #rules: 4
    #arcs: 14/121
    DPs:
     g#(mark(X)) -> g#(X)
     g#(active(X)) -> g#(X)
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     mark(c()) -> active(c())
     mark(f(X)) -> active(f(X))
     mark(g(X)) -> active(g(X))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [g#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [f](x0) = 0,
      
      [g](x0) = 0,
      
      [active](x0) = x0 + 1,
      
      [c] = 0
     orientation:
      g#(mark(X)) = X + 1 >= X = g#(X)
      
      g#(active(X)) = X + 1 >= X = g#(X)
      
      active(c()) = 1 >= 1 = mark(f(g(c())))
      
      active(f(g(X))) = 1 >= 1 = mark(g(X))
      
      mark(c()) = 1 >= 1 = active(c())
      
      mark(f(X)) = 1 >= 1 = active(f(X))
      
      mark(g(X)) = 1 >= 1 = active(g(X))
      
      f(mark(X)) = 0 >= 0 = f(X)
      
      f(active(X)) = 0 >= 0 = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
     problem:
      DPs:
       
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       mark(c()) -> active(c())
       mark(f(X)) -> active(f(X))
       mark(g(X)) -> active(g(X))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Qed
    
    DPs:
     f#(mark(X)) -> f#(X)
     f#(active(X)) -> f#(X)
    TRS:
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
     mark(c()) -> active(c())
     mark(f(X)) -> active(f(X))
     mark(g(X)) -> active(g(X))
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
    Matrix Interpretation Processor:
     dimension: 1
     interpretation:
      [f#](x0) = x0,
      
      [mark](x0) = x0 + 1,
      
      [f](x0) = 0,
      
      [g](x0) = 0,
      
      [active](x0) = x0 + 1,
      
      [c] = 0
     orientation:
      f#(mark(X)) = X + 1 >= X = f#(X)
      
      f#(active(X)) = X + 1 >= X = f#(X)
      
      active(c()) = 1 >= 1 = mark(f(g(c())))
      
      active(f(g(X))) = 1 >= 1 = mark(g(X))
      
      mark(c()) = 1 >= 1 = active(c())
      
      mark(f(X)) = 1 >= 1 = active(f(X))
      
      mark(g(X)) = 1 >= 1 = active(g(X))
      
      f(mark(X)) = 0 >= 0 = f(X)
      
      f(active(X)) = 0 >= 0 = f(X)
      
      g(mark(X)) = 0 >= 0 = g(X)
      
      g(active(X)) = 0 >= 0 = g(X)
     problem:
      DPs:
       
      TRS:
       active(c()) -> mark(f(g(c())))
       active(f(g(X))) -> mark(g(X))
       mark(c()) -> active(c())
       mark(f(X)) -> active(f(X))
       mark(g(X)) -> active(g(X))
       f(mark(X)) -> f(X)
       f(active(X)) -> f(X)
       g(mark(X)) -> g(X)
       g(active(X)) -> g(X)
     Qed