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)
  Matrix Interpretation Processor: dim=1
   
   interpretation:
    [mark#](x0) = 4x0 + 2,
    
    [f#](x0) = x0,
    
    [g#](x0) = x0 + 1,
    
    [active#](x0) = 3x0 + 1,
    
    [mark](x0) = 2x0 + 4,
    
    [f](x0) = 1,
    
    [g](x0) = 0,
    
    [active](x0) = 2x0 + 3,
    
    [c] = 6
   orientation:
    active#(c()) = 19 >= 7 = g#(c())
    
    active#(c()) = 19 >= 0 = f#(g(c()))
    
    active#(c()) = 19 >= 6 = mark#(f(g(c())))
    
    active#(f(g(X))) = 4 >= 2 = mark#(g(X))
    
    mark#(c()) = 26 >= 19 = active#(c())
    
    mark#(f(X)) = 6 >= 4 = active#(f(X))
    
    mark#(g(X)) = 2 >= 1 = active#(g(X))
    
    f#(mark(X)) = 2X + 4 >= X = f#(X)
    
    f#(active(X)) = 2X + 3 >= X = f#(X)
    
    g#(mark(X)) = 2X + 5 >= X + 1 = g#(X)
    
    g#(active(X)) = 2X + 4 >= X + 1 = g#(X)
    
    active(c()) = 15 >= 6 = mark(f(g(c())))
    
    active(f(g(X))) = 5 >= 4 = mark(g(X))
    
    mark(c()) = 16 >= 15 = active(c())
    
    mark(f(X)) = 6 >= 5 = active(f(X))
    
    mark(g(X)) = 4 >= 3 = active(g(X))
    
    f(mark(X)) = 1 >= 1 = f(X)
    
    f(active(X)) = 1 >= 1 = 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