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