YES

Problem:
 active(f(x)) -> mark(f(f(x)))
 chk(no(f(x))) -> f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
 mat(f(x),f(y())) -> f(mat(x,y()))
 chk(no(c())) -> active(c())
 mat(f(x),c()) -> no(c())
 f(active(x)) -> active(f(x))
 f(no(x)) -> no(f(x))
 f(mark(x)) -> mark(f(x))
 tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))

Proof:
 Matrix Interpretation Processor: dim=3
  
  interpretation:
              [1 0 1]     [1]
   [tp](x0) = [0 0 0]x0 + [0]
              [0 1 1]     [1],
   
         [0]
   [c] = [1]
         [0],
   
         [0]
   [y] = [0]
         [1],
   
                   [1 0 0]     [1 1 0]  
   [mat](x0, x1) = [0 0 0]x0 + [0 1 0]x1
                   [0 0 0]     [0 0 0]  ,
   
         [0]
   [X] = [0]
         [0],
   
               [1 0 1]  
   [chk](x0) = [0 1 0]x0
               [0 0 1]  ,
   
                   [1]
   [no](x0) = x0 + [0]
                   [0],
   
                [1 0 0]  
   [mark](x0) = [0 0 1]x0
                [0 1 0]  ,
   
                       [1]
   [active](x0) = x0 + [0]
                       [0],
   
             [1 0 0]  
   [f](x0) = [0 0 1]x0
             [0 1 0]  
  orientation:
                  [1 0 0]    [1]    [1 0 0]                 
   active(f(x)) = [0 0 1]x + [0] >= [0 0 1]x = mark(f(f(x)))
                  [0 1 0]    [0]    [0 1 0]                 
   
                   [1 1 0]    [1]    [1 1 0]                                                    
   chk(no(f(x))) = [0 0 1]x + [0] >= [0 0 0]x = f(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
                   [0 1 0]    [0]    [0 1 0]                                                    
   
                      [1 0 0]    [1]    [1 0 0]                 
   mat(f(x),f(y())) = [0 0 0]x + [1] >= [0 0 0]x = f(mat(x,y()))
                      [0 0 0]    [0]    [0 0 0]                 
   
                  [1]    [1]              
   chk(no(c())) = [1] >= [1] = active(c())
                  [0]    [0]              
   
                   [1 0 0]    [1]    [1]          
   mat(f(x),c()) = [0 0 0]x + [1] >= [1] = no(c())
                   [0 0 0]    [0]    [0]          
   
                  [1 0 0]    [1]    [1 0 0]    [1]               
   f(active(x)) = [0 0 1]x + [0] >= [0 0 1]x + [0] = active(f(x))
                  [0 1 0]    [0]    [0 1 0]    [0]               
   
              [1 0 0]    [1]    [1 0 0]    [1]           
   f(no(x)) = [0 0 1]x + [0] >= [0 0 1]x + [0] = no(f(x))
              [0 1 0]    [0]    [0 1 0]    [0]           
   
                                   
   f(mark(x)) = x >= x = mark(f(x))
                                   
   
                 [1 1 0]    [1]    [1 1 0]    [1]                                                    
   tp(mark(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
                 [0 1 1]    [1]    [0 1 0]    [1]                                                    
  problem:
   chk(no(c())) -> active(c())
   mat(f(x),c()) -> no(c())
   f(active(x)) -> active(f(x))
   f(no(x)) -> no(f(x))
   f(mark(x)) -> mark(f(x))
   tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
  Matrix Interpretation Processor: dim=3
   
   interpretation:
               [1 0 0]     [0]
    [tp](x0) = [0 0 0]x0 + [1]
               [0 0 0]     [0],
    
          [0]
    [c] = [1]
          [0],
    
                    [1 0 0]     [1 1 0]     [0]
    [mat](x0, x1) = [0 0 0]x0 + [0 0 0]x1 + [1]
                    [0 0 0]     [0 0 0]     [1],
    
          [0]
    [X] = [0]
          [0],
    
                [1 0 1]  
    [chk](x0) = [1 0 1]x0
                [0 0 1]  ,
    
               [1 0 0]  
    [no](x0) = [0 0 0]x0
               [0 1 0]  ,
    
                 [1 1 0]     [1]
    [mark](x0) = [0 0 0]x0 + [0]
                 [0 0 0]     [0],
    
                   [1 0 0]  
    [active](x0) = [0 0 0]x0
                   [0 0 0]  ,
    
              [1 0 0]  
    [f](x0) = [0 0 0]x0
              [0 0 0]  
   orientation:
                   [1]    [0]              
    chk(no(c())) = [1] >= [0] = active(c())
                   [1]    [0]              
    
                    [1 0 0]    [1]    [0]          
    mat(f(x),c()) = [0 0 0]x + [1] >= [0] = no(c())
                    [0 0 0]    [1]    [1]          
    
                   [1 0 0]     [1 0 0]                
    f(active(x)) = [0 0 0]x >= [0 0 0]x = active(f(x))
                   [0 0 0]     [0 0 0]                
    
               [1 0 0]     [1 0 0]            
    f(no(x)) = [0 0 0]x >= [0 0 0]x = no(f(x))
               [0 0 0]     [0 0 0]            
    
                 [1 1 0]    [1]    [1 0 0]    [1]             
    f(mark(x)) = [0 0 0]x + [0] >= [0 0 0]x + [0] = mark(f(x))
                 [0 0 0]    [0]    [0 0 0]    [0]             
    
                  [1 1 0]    [1]    [1 1 0]    [1]                                                    
    tp(mark(x)) = [0 0 0]x + [1] >= [0 0 0]x + [1] = tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
                  [0 0 0]    [0]    [0 0 0]    [0]                                                    
   problem:
    f(active(x)) -> active(f(x))
    f(no(x)) -> no(f(x))
    f(mark(x)) -> mark(f(x))
    tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
   Matrix Interpretation Processor: dim=3
    
    interpretation:
                [1 0 0]  
     [tp](x0) = [0 0 0]x0
                [0 0 0]  ,
     
                     [1 0 0]     [1 0 0]  
     [mat](x0, x1) = [0 0 0]x0 + [0 0 0]x1
                     [0 0 0]     [0 0 0]  ,
     
           [0]
     [X] = [0]
           [0],
     
                 [1 0 0]  
     [chk](x0) = [0 0 0]x0
                 [0 0 0]  ,
     
                     [1]
     [no](x0) = x0 + [1]
                     [0],
     
                       [0]
     [mark](x0) = x0 + [1]
                       [1],
     
                    [1 1 0]     [1]
     [active](x0) = [0 1 0]x0 + [0]
                    [0 0 1]     [0],
     
               [1 0 1]  
     [f](x0) = [0 1 0]x0
               [0 1 0]  
    orientation:
                    [1 1 1]    [1]    [1 1 1]    [1]               
     f(active(x)) = [0 1 0]x + [0] >= [0 1 0]x + [0] = active(f(x))
                    [0 1 0]    [0]    [0 1 0]    [0]               
     
                [1 0 1]    [1]    [1 0 1]    [1]           
     f(no(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = no(f(x))
                [0 1 0]    [1]    [0 1 0]    [0]           
     
                  [1 0 1]    [1]    [1 0 1]    [0]             
     f(mark(x)) = [0 1 0]x + [1] >= [0 1 0]x + [1] = mark(f(x))
                  [0 1 0]    [1]    [0 1 0]    [1]             
     
                   [1 0 0]     [1 0 0]                                                     
     tp(mark(x)) = [0 0 0]x >= [0 0 0]x = tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
                   [0 0 0]     [0 0 0]                                                     
    problem:
     f(active(x)) -> active(f(x))
     f(no(x)) -> no(f(x))
     tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
    DP Processor:
     DPs:
      f#(active(x)) -> f#(x)
      f#(no(x)) -> f#(x)
      tp#(mark(x)) -> f#(X())
      tp#(mark(x)) -> f#(f(X()))
      tp#(mark(x)) -> f#(f(f(X())))
      tp#(mark(x)) -> f#(f(f(f(X()))))
      tp#(mark(x)) -> f#(f(f(f(f(X())))))
      tp#(mark(x)) -> f#(f(f(f(f(f(X()))))))
      tp#(mark(x)) -> f#(f(f(f(f(f(f(X())))))))
      tp#(mark(x)) -> f#(f(f(f(f(f(f(f(X()))))))))
      tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(X())))))))))
      tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(f(X()))))))))))
      tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
     TRS:
      f(active(x)) -> active(f(x))
      f(no(x)) -> no(f(x))
      tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
     TDG Processor:
      DPs:
       f#(active(x)) -> f#(x)
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(X())
       tp#(mark(x)) -> f#(f(X()))
       tp#(mark(x)) -> f#(f(f(X())))
       tp#(mark(x)) -> f#(f(f(f(X()))))
       tp#(mark(x)) -> f#(f(f(f(f(X())))))
       tp#(mark(x)) -> f#(f(f(f(f(f(X()))))))
       tp#(mark(x)) -> f#(f(f(f(f(f(f(X())))))))
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(X()))))))))
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(X())))))))))
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(f(X()))))))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
      TRS:
       f(active(x)) -> active(f(x))
       f(no(x)) -> no(f(x))
       tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
      graph:
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(f(X()))))))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(X())))))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(X()))))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(f(f(X())))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(f(X()))))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(f(X())))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(f(X()))))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(f(X())))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(f(X()))
       tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x))) ->
       tp#(mark(x)) -> f#(X())
       tp#(mark(x)) -> f#(X()) -> f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(X()) -> f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(X())) -> f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(X())) -> f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(X()))) -> f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(X()))) -> f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(X())))) -> f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(X())))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(X()))))) -> f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(X()))))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(X())))))) ->
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(X())))))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(X()))))))) ->
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(X()))))))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(X())))))))) ->
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(X())))))))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(X()))))))))) ->
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(X()))))))))) ->
       f#(active(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(f(X())))))))))) ->
       f#(no(x)) -> f#(x)
       tp#(mark(x)) -> f#(f(f(f(f(f(f(f(f(f(X())))))))))) ->
       f#(active(x)) -> f#(x)
       f#(no(x)) -> f#(x) -> f#(no(x)) -> f#(x)
       f#(no(x)) -> f#(x) -> f#(active(x)) -> f#(x)
       f#(active(x)) -> f#(x) -> f#(no(x)) -> f#(x)
       f#(active(x)) -> f#(x) -> f#(active(x)) -> f#(x)
      SCC Processor:
       #sccs: 2
       #rules: 3
       #arcs: 35/169
       DPs:
        tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
       TRS:
        f(active(x)) -> active(f(x))
        f(no(x)) -> no(f(x))
        tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
       EDG Processor:
        DPs:
         tp#(mark(x)) -> tp#(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        TRS:
         f(active(x)) -> active(f(x))
         f(no(x)) -> no(f(x))
         tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        graph:
         
        Qed
       
       DPs:
        f#(active(x)) -> f#(x)
        f#(no(x)) -> f#(x)
       TRS:
        f(active(x)) -> active(f(x))
        f(no(x)) -> no(f(x))
        tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
       Subterm Criterion Processor:
        simple projection:
         pi(f#) = 0
        problem:
         DPs:
          
         TRS:
          f(active(x)) -> active(f(x))
          f(no(x)) -> no(f(x))
          tp(mark(x)) -> tp(chk(mat(f(f(f(f(f(f(f(f(f(f(X())))))))))),x)))
        Qed