YES(?,O(n^2))
TRS:
 {
    a__c X -> d X,
    a__c X -> c X,
    a__f X -> f X,
  a__f f X -> a__c f g f X,
    a__h X -> h X,
    a__h X -> a__c d X,
  mark f X -> a__f mark X,
  mark g X -> g X,
  mark h X -> a__h mark X,
  mark d X -> d X,
  mark c X -> a__c X
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      a__c X -> d X,
      a__c X -> c X,
      a__f X -> f X,
    a__f f X -> a__c f g f X,
      a__h X -> h X,
      a__h X -> a__c d X,
    mark f X -> a__f mark X,
    mark g X -> g X,
    mark h X -> a__h mark X,
    mark d X -> d X,
    mark c X -> a__c X
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [0]
   [c]([X0]) = [0 0][X0] + [1]
   
          [X1]    [1 2][X1]   [1]
   [mark]([X0]) = [0 1][X0] + [0]
   
          [X1]    [1 2][X1]   [3]
   [a__h]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [0]
   [d]([X0]) = [0 0][X0] + [0]
   
          [X1]    [1 2][X1]   [1]
   [a__f]([X0]) = [0 1][X0] + [1]
   
          [X1]    [1 0][X1]   [2]
   [a__c]([X0]) = [0 0][X0] + [1]
   
       [X1]    [1 2][X1]   [2]
   [h]([X0]) = [0 1][X0] + [1]
   
       [X1]    [1 0][X1]   [0]
   [g]([X0]) = [0 0][X0] + [0]
   
       [X1]    [1 2][X1]   [0]
   [f]([X0]) = [0 1][X0] + [1]
   
   
   Qed