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))
  TDG 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))
   graph:
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
    top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
    top#(ok(X)) -> top#(active(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
    top#(ok(X)) -> active#(X) -> active#(c()) -> f#(g(c()))
    top#(ok(X)) -> active#(X) -> active#(c()) -> g#(c())
    top#(mark(X)) -> top#(proper(X)) ->
    top#(ok(X)) -> top#(active(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
    top#(mark(X)) -> top#(proper(X)) ->
    top#(mark(X)) -> top#(proper(X))
    top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
    proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    active#(c()) -> f#(g(c())) -> f#(ok(X)) -> f#(X)
    active#(c()) -> g#(c()) -> g#(ok(X)) -> g#(X)
   EDG 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))
    graph:
     top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
     top#(ok(X)) -> top#(active(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
     top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> top#(active(X))
     top#(ok(X)) -> active#(X) -> active#(c()) -> g#(c())
     top#(ok(X)) -> active#(X) -> active#(c()) -> f#(g(c()))
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> proper#(X)
     top#(mark(X)) -> top#(proper(X)) ->
     top#(mark(X)) -> top#(proper(X))
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
     top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
     top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
     proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(f(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
     proper#(f(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
     proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
     proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> proper#(X)
     proper#(g(X)) -> proper#(X) -> proper#(f(X)) -> f#(proper(X))
     proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
     proper#(g(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
     proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
     f#(ok(X)) -> f#(X) -> f#(ok(X)) -> f#(X)
     g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    CDG 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))
     graph:
      top#(ok(X)) -> top#(active(X)) ->
      top#(ok(X)) -> top#(active(X))
      top#(ok(X)) -> top#(active(X)) -> top#(ok(X)) -> active#(X)
      top#(ok(X)) -> top#(active(X)) ->
      top#(mark(X)) -> top#(proper(X))
      top#(ok(X)) -> top#(active(X)) -> top#(mark(X)) -> proper#(X)
      top#(mark(X)) -> top#(proper(X)) ->
      top#(ok(X)) -> top#(active(X))
      top#(mark(X)) -> top#(proper(X)) -> top#(ok(X)) -> active#(X)
      top#(mark(X)) -> top#(proper(X)) ->
      top#(mark(X)) -> top#(proper(X))
      top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
      proper#(f(X)) -> f#(proper(X)) -> f#(ok(X)) -> f#(X)
      proper#(g(X)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
     SCC Processor:
      #sccs: 1
      #rules: 2
      #arcs: 10/144
      DPs:
       top#(ok(X)) -> top#(active(X))
       top#(mark(X)) -> top#(proper(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))
      Matrix Interpretation Processor: dim=2
       
       interpretation:
        [top#](x0) = [2 0]x0,
        
                    [0]
        [top](x0) = [0],
        
                   [0 2]     [1]
        [ok](x0) = [0 0]x0 + [0],
        
                       [0 2]     [1]
        [proper](x0) = [0 0]x0 + [1],
        
                     [0 2]     [2]
        [mark](x0) = [1 1]x0 + [0],
        
                  [3]
        [f](x0) = [1],
        
                  [1]
        [g](x0) = [0],
        
                       [0 2]  
        [active](x0) = [2 1]x0,
        
              [1]
        [c] = [2]
       orientation:
        top#(ok(X)) = [0 4]X + [2] >= [0 4]X = top#(active(X))
        
        top#(mark(X)) = [0 4]X + [4] >= [0 4]X + [2] = top#(proper(X))
        
                      [4]    [4]                  
        active(c()) = [4] >= [4] = mark(f(g(c())))
        
                          [2]    [2]             
        active(f(g(X))) = [7] >= [1] = mark(g(X))
        
                      [5]    [5]          
        proper(c()) = [1] >= [0] = ok(c())
        
                       [3]    [3]               
        proper(f(X)) = [1] >= [1] = f(proper(X))
        
                       [1]    [1]               
        proper(g(X)) = [1] >= [0] = g(proper(X))
        
                   [3]    [3]           
        f(ok(X)) = [1] >= [0] = ok(f(X))
        
                   [1]    [1]           
        g(ok(X)) = [0] >= [0] = ok(g(X))
        
                       [0]    [0]                 
        top(mark(X)) = [0] >= [0] = top(proper(X))
        
                     [0]    [0]                 
        top(ok(X)) = [0] >= [0] = top(active(X))
       problem:
        DPs:
         
        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))
       Qed