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))
  TDG 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))
   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#(h(d())) -> g#(c())
    top#(ok(X)) -> active#(X) -> active#(g(X)) -> h#(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)
    top#(mark(X)) -> proper#(X) -> proper#(h(X)) -> h#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(h(X)) -> proper#(X)
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    top#(mark(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(h(X)) -> proper#(X) -> proper#(h(X)) -> h#(proper(X))
    proper#(h(X)) -> proper#(X) -> proper#(h(X)) -> proper#(X)
    proper#(h(X)) -> proper#(X) -> proper#(g(X)) -> g#(proper(X))
    proper#(h(X)) -> proper#(X) -> proper#(g(X)) -> proper#(X)
    proper#(h(X)) -> h#(proper(X)) -> h#(ok(X)) -> h#(X)
    proper#(g(X)) -> proper#(X) -> proper#(h(X)) -> h#(proper(X))
    proper#(g(X)) -> proper#(X) -> proper#(h(X)) -> proper#(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)) -> g#(proper(X)) -> g#(ok(X)) -> g#(X)
    g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
    h#(ok(X)) -> h#(X) -> h#(ok(X)) -> h#(X)
    active#(h(d())) -> g#(c()) -> g#(ok(X)) -> g#(X)
    active#(g(X)) -> h#(X) -> h#(ok(X)) -> h#(X)
   SCC Processor:
    #sccs: 4
    #rules: 6
    #arcs: 28/144
    DPs:
     top#(ok(X)) -> top#(active(X))
     top#(mark(X)) -> top#(proper(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=3
     
     interpretation:
      [top#](x0) = [0 0 1]x0,
      
                  [0]
      [top](x0) = [0]
                  [0],
      
                 [1 1 0]  
      [ok](x0) = [1 0 0]x0
                 [0 1 1]  ,
      
                     [1 1 0]  
      [proper](x0) = [1 0 0]x0
                     [0 1 1]  ,
      
            [1]
      [d] = [0]
            [0],
      
            [0]
      [c] = [0]
            [1],
      
                   [0 0 0]     [0]
      [mark](x0) = [0 0 1]x0 + [1]
                   [0 1 1]     [1],
      
                [1 1 0]  
      [h](x0) = [1 0 0]x0
                [1 1 0]  ,
      
                     [0 0 0]  
      [active](x0) = [1 0 1]x0
                     [0 1 1]  ,
      
                [1 1 0]     [0]
      [g](x0) = [1 0 0]x0 + [0]
                [1 1 0]     [1]
     orientation:
      top#(ok(X)) = [0 1 1]X >= [0 1 1]X = top#(active(X))
      
      top#(mark(X)) = [0 1 1]X + [1] >= [0 1 1]X = top#(proper(X))
      
                     [0 0 0]    [0]    [0 0 0]    [0]             
      active(g(X)) = [2 2 0]X + [1] >= [1 1 0]X + [1] = mark(h(X))
                     [2 1 0]    [1]    [2 1 0]    [1]             
      
                    [0]    [0]            
      active(c()) = [1] >= [1] = mark(d())
                    [1]    [1]            
      
                       [0]    [0]               
      active(h(d())) = [2] >= [2] = mark(g(c()))
                       [2]    [2]               
      
                     [2 1 0]    [0]    [2 1 0]    [0]               
      proper(g(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = g(proper(X))
                     [2 1 0]    [1]    [2 1 0]    [1]               
      
                     [2 1 0]     [2 1 0]                
      proper(h(X)) = [1 1 0]X >= [1 1 0]X = h(proper(X))
                     [2 1 0]     [2 1 0]                
      
                    [0]    [0]          
      proper(c()) = [0] >= [0] = ok(c())
                    [1]    [1]          
      
                    [1]    [1]          
      proper(d()) = [1] >= [1] = ok(d())
                    [0]    [0]          
      
                 [2 1 0]    [0]    [2 1 0]    [0]           
      g(ok(X)) = [1 1 0]X + [0] >= [1 1 0]X + [0] = ok(g(X))
                 [2 1 0]    [1]    [2 1 0]    [1]           
      
                 [2 1 0]     [2 1 0]            
      h(ok(X)) = [1 1 0]X >= [1 1 0]X = ok(h(X))
                 [2 1 0]     [2 1 0]            
      
                     [0]    [0]                 
      top(mark(X)) = [0] >= [0] = top(proper(X))
                     [0]    [0]                 
      
                   [0]    [0]                 
      top(ok(X)) = [0] >= [0] = top(active(X))
                   [0]    [0]                 
     problem:
      DPs:
       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))
     Arctic Interpretation Processor:
      dimension: 1
      interpretation:
       [top#](x0) = x0 + 0,
       
       [top](x0) = 0,
       
       [ok](x0) = x0 + 1,
       
       [proper](x0) = x0,
       
       [d] = 2,
       
       [c] = 1,
       
       [mark](x0) = 0,
       
       [h](x0) = x0 + 0,
       
       [active](x0) = 0,
       
       [g](x0) = 2x0 + 0
      orientation:
       top#(ok(X)) = X + 1 >= 0 = top#(active(X))
       
       active(g(X)) = 0 >= 0 = mark(h(X))
       
       active(c()) = 0 >= 0 = mark(d())
       
       active(h(d())) = 0 >= 0 = mark(g(c()))
       
       proper(g(X)) = 2X + 0 >= 2X + 0 = g(proper(X))
       
       proper(h(X)) = X + 0 >= X + 0 = h(proper(X))
       
       proper(c()) = 1 >= 1 = ok(c())
       
       proper(d()) = 2 >= 2 = ok(d())
       
       g(ok(X)) = 2X + 3 >= 2X + 1 = ok(g(X))
       
       h(ok(X)) = X + 1 >= X + 1 = ok(h(X))
       
       top(mark(X)) = 0 >= 0 = top(proper(X))
       
       top(ok(X)) = 0 >= 0 = 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
    
    DPs:
     proper#(g(X)) -> proper#(X)
     proper#(h(X)) -> proper#(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))
    Subterm Criterion Processor:
     simple projection:
      pi(proper#) = 0
     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
    
    DPs:
     h#(ok(X)) -> h#(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))
    Subterm Criterion Processor:
     simple projection:
      pi(h#) = 0
     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
    
    DPs:
     g#(ok(X)) -> g#(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))
    Subterm Criterion Processor:
     simple projection:
      pi(g#) = 0
     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