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:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
               [1 0 1]  
   [top](x0) = [0 0 0]x0
               [0 0 0]  ,
   
              [1 1 0]  
   [ok](x0) = [0 0 0]x0
              [0 0 1]  ,
   
                  [1 0 0]  
   [proper](x0) = [0 0 0]x0
                  [0 0 1]  ,
   
         [1]
   [d] = [0]
         [0],
   
         [0]
   [c] = [0]
         [1],
   
                [1 0 1]     [0]
   [mark](x0) = [0 0 0]x0 + [1]
                [0 0 0]     [0],
   
             [1 0 0]  
   [h](x0) = [0 0 0]x0
             [0 0 0]  ,
   
                  [1 0 1]     [0]
   [active](x0) = [0 0 0]x0 + [1]
                  [0 0 0]     [0],
   
             [1 0 0]     [0]
   [g](x0) = [0 0 0]x0 + [0]
             [0 0 0]     [1]
  orientation:
                  [1 0 0]    [1]    [1 0 0]    [0]             
   active(g(X)) = [0 0 0]X + [1] >= [0 0 0]X + [1] = mark(h(X))
                  [0 0 0]    [0]    [0 0 0]    [0]             
   
                 [1]    [1]            
   active(c()) = [1] >= [1] = mark(d())
                 [0]    [0]            
   
                    [1]    [1]               
   active(h(d())) = [1] >= [1] = mark(g(c()))
                    [0]    [0]               
   
                  [1 0 0]    [0]    [1 0 0]    [0]               
   proper(g(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = g(proper(X))
                  [0 0 0]    [1]    [0 0 0]    [1]               
   
                  [1 0 0]     [1 0 0]                
   proper(h(X)) = [0 0 0]X >= [0 0 0]X = h(proper(X))
                  [0 0 0]     [0 0 0]                
   
                 [0]    [0]          
   proper(c()) = [0] >= [0] = ok(c())
                 [1]    [1]          
   
                 [1]    [1]          
   proper(d()) = [0] >= [0] = ok(d())
                 [0]    [0]          
   
              [1 1 0]    [0]    [1 0 0]    [0]           
   g(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(g(X))
              [0 0 0]    [1]    [0 0 0]    [1]           
   
              [1 1 0]     [1 0 0]            
   h(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(h(X))
              [0 0 0]     [0 0 0]            
   
                  [1 0 1]     [1 0 1]                  
   top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X))
                  [0 0 0]     [0 0 0]                  
   
                [1 1 1]     [1 0 1]                  
   top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                [0 0 0]     [0 0 0]                  
  problem:
   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:
                [1 0 1]  
    [top](x0) = [0 0 0]x0
                [0 0 0]  ,
    
               [1 0 1]  
    [ok](x0) = [0 0 0]x0
               [0 1 0]  ,
    
                   [1 0 1]  
    [proper](x0) = [0 0 0]x0
                   [0 1 0]  ,
    
          [0]
    [d] = [1]
          [0],
    
          [0]
    [c] = [0]
          [1],
    
                 [1 0 0]  
    [mark](x0) = [0 0 0]x0
                 [0 1 1]  ,
    
                   [1]
    [h](x0) = x0 + [0]
                   [0],
    
                   [1 0 0]  
    [active](x0) = [0 0 1]x0
                   [0 1 1]  ,
    
                
    [g](x0) = x0
                
   orientation:
                  [0]    [0]            
    active(c()) = [1] >= [0] = mark(d())
                  [1]    [1]            
    
                     [1]    [0]               
    active(h(d())) = [0] >= [0] = mark(g(c()))
                     [1]    [1]               
    
                   [1 0 1]     [1 0 1]                
    proper(g(X)) = [0 0 0]X >= [0 0 0]X = g(proper(X))
                   [0 1 0]     [0 1 0]                
    
                   [1 0 1]    [1]    [1 0 1]    [1]               
    proper(h(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = h(proper(X))
                   [0 1 0]    [0]    [0 1 0]    [0]               
    
                  [1]    [1]          
    proper(c()) = [0] >= [0] = ok(c())
                  [0]    [0]          
    
                  [0]    [0]          
    proper(d()) = [0] >= [0] = ok(d())
                  [1]    [1]          
    
               [1 0 1]     [1 0 1]            
    g(ok(X)) = [0 0 0]X >= [0 0 0]X = ok(g(X))
               [0 1 0]     [0 1 0]            
    
               [1 0 1]    [1]    [1 0 1]    [1]           
    h(ok(X)) = [0 0 0]X + [0] >= [0 0 0]X + [0] = ok(h(X))
               [0 1 0]    [0]    [0 1 0]    [0]           
    
                   [1 1 1]     [1 1 1]                  
    top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X))
                   [0 0 0]     [0 0 0]                  
    
                 [1 1 1]     [1 1 1]                  
    top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                 [0 0 0]     [0 0 0]                  
   problem:
    active(c()) -> mark(d())
    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:
                 [1 0 0]  
     [top](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                [1 0 0]  
     [ok](x0) = [0 0 1]x0
                [0 0 1]  ,
     
                    [1 1 0]  
     [proper](x0) = [0 1 0]x0
                    [1 1 0]  ,
     
           [0]
     [d] = [0]
           [0],
     
           [1]
     [c] = [0]
           [0],
     
                  [1 1 0]  
     [mark](x0) = [0 0 0]x0
                  [0 0 0]  ,
     
               [1 0 0]     [0]
     [h](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [1],
     
                    [1 0 0]  
     [active](x0) = [0 0 0]x0
                    [0 0 0]  ,
     
               [1 0 0]     [0]
     [g](x0) = [0 1 0]x0 + [1]
               [0 0 0]     [0]
    orientation:
                   [1]    [0]            
     active(c()) = [0] >= [0] = mark(d())
                   [0]    [0]            
     
                    [1 1 0]    [1]    [1 1 0]    [0]               
     proper(g(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = g(proper(X))
                    [1 1 0]    [1]    [0 0 0]    [0]               
     
                    [1 1 0]    [1]    [1 1 0]    [0]               
     proper(h(X)) = [0 1 0]X + [1] >= [0 1 0]X + [1] = h(proper(X))
                    [1 1 0]    [1]    [0 0 0]    [1]               
     
                   [1]    [1]          
     proper(c()) = [0] >= [0] = ok(c())
                   [1]    [0]          
     
                   [0]    [0]          
     proper(d()) = [0] >= [0] = ok(d())
                   [0]    [0]          
     
                [1 0 0]    [0]    [1 0 0]            
     g(ok(X)) = [0 0 1]X + [1] >= [0 0 0]X = ok(g(X))
                [0 0 0]    [0]    [0 0 0]            
     
                [1 0 0]    [0]    [1 0 0]    [0]           
     h(ok(X)) = [0 0 1]X + [1] >= [0 0 0]X + [1] = ok(h(X))
                [0 0 0]    [1]    [0 0 0]    [1]           
     
                    [1 1 0]     [1 1 0]                  
     top(mark(X)) = [0 0 0]X >= [0 0 0]X = top(proper(X))
                    [0 0 0]     [0 0 0]                  
     
                  [1 0 0]     [1 0 0]                  
     top(ok(X)) = [0 0 0]X >= [0 0 0]X = top(active(X))
                  [0 0 0]     [0 0 0]                  
    problem:
     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=1
     
     interpretation:
      [top](x0) = x0 + 2,
      
      [ok](x0) = x0 + 1,
      
      [proper](x0) = x0 + 1,
      
      [d] = 0,
      
      [c] = 7,
      
      [mark](x0) = x0 + 1,
      
      [h](x0) = x0 + 7,
      
      [active](x0) = x0,
      
      [g](x0) = x0 + 2
     orientation:
      proper(c()) = 8 >= 8 = ok(c())
      
      proper(d()) = 1 >= 1 = ok(d())
      
      g(ok(X)) = X + 3 >= X + 3 = ok(g(X))
      
      h(ok(X)) = X + 8 >= X + 8 = ok(h(X))
      
      top(mark(X)) = X + 3 >= X + 3 = top(proper(X))
      
      top(ok(X)) = X + 3 >= X + 2 = top(active(X))
     problem:
      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))
     DP Processor:
      DPs:
       g#(ok(X)) -> g#(X)
       h#(ok(X)) -> h#(X)
       top#(mark(X)) -> proper#(X)
       top#(mark(X)) -> top#(proper(X))
      TRS:
       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))
      TDG Processor:
       DPs:
        g#(ok(X)) -> g#(X)
        h#(ok(X)) -> h#(X)
        top#(mark(X)) -> proper#(X)
        top#(mark(X)) -> top#(proper(X))
       TRS:
        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))
       graph:
        top#(mark(X)) -> top#(proper(X)) ->
        top#(mark(X)) -> top#(proper(X))
        top#(mark(X)) -> top#(proper(X)) -> top#(mark(X)) -> proper#(X)
        h#(ok(X)) -> h#(X) -> h#(ok(X)) -> h#(X)
        g#(ok(X)) -> g#(X) -> g#(ok(X)) -> g#(X)
       SCC Processor:
        #sccs: 3
        #rules: 3
        #arcs: 4/16
        DPs:
         g#(ok(X)) -> g#(X)
        TRS:
         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))
        Subterm Criterion Processor:
         simple projection:
          pi(g#) = 0
         problem:
          DPs:
           
          TRS:
           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))
         Qed
        
        DPs:
         h#(ok(X)) -> h#(X)
        TRS:
         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))
        Subterm Criterion Processor:
         simple projection:
          pi(h#) = 0
         problem:
          DPs:
           
          TRS:
           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))
         Qed
        
        DPs:
         top#(mark(X)) -> top#(proper(X))
        TRS:
         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))
        EDG Processor:
         DPs:
          top#(mark(X)) -> top#(proper(X))
         TRS:
          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))
         graph:
          
         Qed