YES

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

Proof:
 DP Processor:
  DPs:
   active#(g(X)) -> h#(X)
   active#(h(d())) -> g#(c())
   proper#(g(X)) -> proper#(X)
   proper#(g(X)) -> g#(proper(X))
   proper#(h(X)) -> proper#(X)
   proper#(h(X)) -> h#(proper(X))
   g#(ok(X)) -> g#(X)
   h#(ok(X)) -> h#(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(g(X)) -> mark(h(X))
   active(c()) -> mark(d())
   active(h(d())) -> mark(g(c()))
   proper(g(X)) -> g(proper(X))
   proper(h(X)) -> h(proper(X))
   proper(c()) -> ok(c())
   proper(d()) -> ok(d())
   g(ok(X)) -> ok(g(X))
   h(ok(X)) -> ok(h(X))
   top(mark(X)) -> top(proper(X))
   top(ok(X)) -> top(active(X))
  Matrix Interpretation Processor: dim=2
   
   interpretation:
    [top#](x0) = [0 1]x0,
    
    [proper#](x0) = [0 1]x0 + [1],
    
    [g#](x0) = [0 1]x0,
    
    [h#](x0) = [0 1]x0,
    
    [active#](x0) = [0 1]x0,
    
                [0 2]     [0]
    [top](x0) = [0 1]x0 + [2],
    
                    [0]
    [ok](x0) = x0 + [1],
    
                        [0]
    [proper](x0) = x0 + [1],
    
          [2]
    [d] = [0],
    
          [0]
    [c] = [2],
    
                 [0 0]     [0]
    [mark](x0) = [0 1]x0 + [2],
    
              [0 0]     [0]
    [h](x0) = [3 1]x0 + [1],
    
                   [0 0]  
    [active](x0) = [0 1]x0,
    
              [0 0]     [0]
    [g](x0) = [3 1]x0 + [3]
   orientation:
    active#(g(X)) = [3 1]X + [3] >= [0 1]X = h#(X)
    
    active#(h(d())) = 7 >= 2 = g#(c())
    
    proper#(g(X)) = [3 1]X + [4] >= [0 1]X + [1] = proper#(X)
    
    proper#(g(X)) = [3 1]X + [4] >= [0 1]X + [1] = g#(proper(X))
    
    proper#(h(X)) = [3 1]X + [2] >= [0 1]X + [1] = proper#(X)
    
    proper#(h(X)) = [3 1]X + [2] >= [0 1]X + [1] = h#(proper(X))
    
    g#(ok(X)) = [0 1]X + [1] >= [0 1]X = g#(X)
    
    h#(ok(X)) = [0 1]X + [1] >= [0 1]X = h#(X)
    
    top#(mark(X)) = [0 1]X + [2] >= [0 1]X + [1] = proper#(X)
    
    top#(mark(X)) = [0 1]X + [2] >= [0 1]X + [1] = top#(proper(X))
    
    top#(ok(X)) = [0 1]X + [1] >= [0 1]X = active#(X)
    
    top#(ok(X)) = [0 1]X + [1] >= [0 1]X = top#(active(X))
    
                   [0 0]    [0]    [0 0]    [0]             
    active(g(X)) = [3 1]X + [3] >= [3 1]X + [3] = mark(h(X))
    
                  [0]    [0]            
    active(c()) = [2] >= [2] = mark(d())
    
                     [0]    [0]               
    active(h(d())) = [7] >= [7] = mark(g(c()))
    
                   [0 0]    [0]    [0 0]    [0]               
    proper(g(X)) = [3 1]X + [4] >= [3 1]X + [4] = g(proper(X))
    
                   [0 0]    [0]    [0 0]    [0]               
    proper(h(X)) = [3 1]X + [2] >= [3 1]X + [2] = h(proper(X))
    
                  [0]    [0]          
    proper(c()) = [3] >= [3] = ok(c())
    
                  [2]    [2]          
    proper(d()) = [1] >= [1] = ok(d())
    
               [0 0]    [0]    [0 0]    [0]           
    g(ok(X)) = [3 1]X + [4] >= [3 1]X + [4] = ok(g(X))
    
               [0 0]    [0]    [0 0]    [0]           
    h(ok(X)) = [3 1]X + [2] >= [3 1]X + [2] = ok(h(X))
    
                   [0 2]    [4]    [0 2]    [2]                 
    top(mark(X)) = [0 1]X + [4] >= [0 1]X + [3] = top(proper(X))
    
                 [0 2]    [2]    [0 2]    [0]                 
    top(ok(X)) = [0 1]X + [3] >= [0 1]X + [2] = top(active(X))
   problem:
    DPs:
     
    TRS:
     active(g(X)) -> mark(h(X))
     active(c()) -> mark(d())
     active(h(d())) -> mark(g(c()))
     proper(g(X)) -> g(proper(X))
     proper(h(X)) -> h(proper(X))
     proper(c()) -> ok(c())
     proper(d()) -> ok(d())
     g(ok(X)) -> ok(g(X))
     h(ok(X)) -> ok(h(X))
     top(mark(X)) -> top(proper(X))
     top(ok(X)) -> top(active(X))
   Qed