YES

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

Proof:
 DP Processor:
  DPs:
   active#(c()) -> g#(c())
   active#(c()) -> f#(g(c()))
   proper#(f(X)) -> proper#(X)
   proper#(f(X)) -> f#(proper(X))
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   f#(ok(X)) -> f#(X)
   g#(ok(X)) -> g#(X)
   top#(mark(X)) -> proper#(X)
   top#(mark(X)) -> top#(proper(X))
   top#(ok(X)) -> active#(X)
   top#(ok(X)) -> top#(active(X))
  TRS:
   active(c()) -> mark(f(g(c())))
   active(f(g(X))) -> mark(g(X))
   proper(c()) -> ok(c())
   proper(f(X)) -> f(proper(X))
   proper(g(X)) -> g(proper(X))
   f(ok(X)) -> ok(f(X))
   g(ok(X)) -> ok(g(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Usable Rule Processor:
   DPs:
    active#(c()) -> g#(c())
    active#(c()) -> f#(g(c()))
    proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X))
    f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X)
    top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X))
   TRS:
    proper(c()) -> ok(c())
    proper(f(X)) -> f(proper(X))
    proper(g(X)) -> g(proper(X))
    f(ok(X)) -> ok(f(X))
    g(ok(X)) -> ok(g(X))
    active(c()) -> mark(f(g(c())))
    active(f(g(X))) -> mark(g(X))
   Matrix Interpretation Processor: dim=2
    
    usable rules:
     proper(c()) -> ok(c())
     proper(f(X)) -> f(proper(X))
     proper(g(X)) -> g(proper(X))
     f(ok(X)) -> ok(f(X))
     g(ok(X)) -> ok(g(X))
     active(c()) -> mark(f(g(c())))
     active(f(g(X))) -> mark(g(X))
    interpretation:
     [top#](x0) = [1 2]x0,
     
     [proper#](x0) = [1 0]x0 + [3],
     
     [f#](x0) = [1 0]x0,
     
     [g#](x0) = [1 0]x0 + [1],
     
     [active#](x0) = [2 1]x0,
     
                [2 0]     [1]
     [ok](x0) = [0 2]x0 + [2],
     
                    [2 0]     [1]
     [proper](x0) = [0 2]x0 + [2],
     
                  [2 0]     [0]
     [mark](x0) = [0 2]x0 + [3],
     
               [2 0]     [1]
     [f](x0) = [0 1]x0 + [0],
     
               [2 0]     [1]
     [g](x0) = [2 0]x0 + [0],
     
                    [0 2]     [2]
     [active](x0) = [1 1]x0 + [1],
     
           [0]
     [c] = [2]
    orientation:
     active#(c()) = 2 >= 1 = g#(c())
     
     active#(c()) = 2 >= 1 = f#(g(c()))
     
     proper#(f(X)) = [2 0]X + [4] >= [1 0]X + [3] = proper#(X)
     
     proper#(f(X)) = [2 0]X + [4] >= [2 0]X + [1] = f#(proper(X))
     
     proper#(g(X)) = [2 0]X + [4] >= [1 0]X + [3] = proper#(X)
     
     proper#(g(X)) = [2 0]X + [4] >= [2 0]X + [2] = g#(proper(X))
     
     f#(ok(X)) = [2 0]X + [1] >= [1 0]X = f#(X)
     
     g#(ok(X)) = [2 0]X + [2] >= [1 0]X + [1] = g#(X)
     
     top#(mark(X)) = [2 4]X + [6] >= [1 0]X + [3] = proper#(X)
     
     top#(mark(X)) = [2 4]X + [6] >= [2 4]X + [5] = top#(proper(X))
     
     top#(ok(X)) = [2 4]X + [5] >= [2 1]X = active#(X)
     
     top#(ok(X)) = [2 4]X + [5] >= [2 4]X + [4] = top#(active(X))
     
                   [1]    [1]          
     proper(c()) = [6] >= [6] = ok(c())
     
                    [4 0]    [3]    [4 0]    [3]               
     proper(f(X)) = [0 2]X + [2] >= [0 2]X + [2] = f(proper(X))
     
                    [4 0]    [3]    [4 0]    [3]               
     proper(g(X)) = [4 0]X + [2] >= [4 0]X + [2] = g(proper(X))
     
                [4 0]    [3]    [4 0]    [3]           
     f(ok(X)) = [0 2]X + [2] >= [0 2]X + [2] = ok(f(X))
     
                [4 0]    [3]    [4 0]    [3]           
     g(ok(X)) = [4 0]X + [2] >= [4 0]X + [2] = ok(g(X))
     
                   [6]    [6]                  
     active(c()) = [3] >= [3] = mark(f(g(c())))
     
                       [4 0]    [2]    [4 0]    [2]             
     active(f(g(X))) = [6 0]X + [4] >= [4 0]X + [3] = mark(g(X))
    problem:
     DPs:
      
     TRS:
      proper(c()) -> ok(c())
      proper(f(X)) -> f(proper(X))
      proper(g(X)) -> g(proper(X))
      f(ok(X)) -> ok(f(X))
      g(ok(X)) -> ok(g(X))
      active(c()) -> mark(f(g(c())))
      active(f(g(X))) -> mark(g(X))
    Qed