YES

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

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