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)
  Usable Rule 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:
    g(mark(X)) -> g(X)
    g(active(X)) -> g(X)
    f(mark(X)) -> f(X)
    f(active(X)) -> f(X)
   Matrix Interpretation Processor: dim=1
    
    usable rules:
     g(mark(X)) -> g(X)
     g(active(X)) -> g(X)
     f(mark(X)) -> f(X)
     f(active(X)) -> f(X)
    interpretation:
     [mark#](x0) = 5x0 + 5,
     
     [f#](x0) = 2x0 + 2,
     
     [g#](x0) = 2x0 + 6,
     
     [active#](x0) = 3x0 + 6,
     
     [mark](x0) = 6x0 + 1,
     
     [f](x0) = x0 + 2,
     
     [g](x0) = 1,
     
     [active](x0) = 4x0 + 4,
     
     [c] = 5
    orientation:
     active#(c()) = 21 >= 16 = g#(c())
     
     active#(c()) = 21 >= 4 = f#(g(c()))
     
     active#(c()) = 21 >= 20 = mark#(f(g(c())))
     
     active#(f(g(X))) = 15 >= 10 = mark#(g(X))
     
     mark#(c()) = 30 >= 21 = active#(c())
     
     mark#(f(X)) = 5X + 15 >= 3X + 12 = active#(f(X))
     
     mark#(g(X)) = 10 >= 9 = active#(g(X))
     
     f#(mark(X)) = 12X + 4 >= 2X + 2 = f#(X)
     
     f#(active(X)) = 8X + 10 >= 2X + 2 = f#(X)
     
     g#(mark(X)) = 12X + 8 >= 2X + 6 = g#(X)
     
     g#(active(X)) = 8X + 14 >= 2X + 6 = g#(X)
     
     g(mark(X)) = 1 >= 1 = g(X)
     
     g(active(X)) = 1 >= 1 = g(X)
     
     f(mark(X)) = 6X + 3 >= X + 2 = f(X)
     
     f(active(X)) = 4X + 6 >= X + 2 = f(X)
    problem:
     DPs:
      
     TRS:
      g(mark(X)) -> g(X)
      g(active(X)) -> g(X)
      f(mark(X)) -> f(X)
      f(active(X)) -> f(X)
    Qed