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) -> a__c(d(X)),
     a__h(X) -> h(X),
  mark(f(X)) -> a__f(mark(X)),
  mark(g(X)) -> g(X),
  mark(d(X)) -> d(X),
  mark(c(X)) -> a__c(X),
  mark(h(X)) -> a__h(mark(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) -> a__c(d(X)),
       a__h(X) -> h(X),
    mark(f(X)) -> a__f(mark(X)),
    mark(g(X)) -> g(X),
    mark(d(X)) -> d(X),
    mark(c(X)) -> a__c(X),
    mark(h(X)) -> a__h(mark(X))
   }
  Matrix Interpretation:
   Interpretation class: triangular
       [X1]    [1 0][X1]   [0]
   [h]([X0]) = [0 1][X0] + [3]
   
       [X1]    [1 0][X1]   [0]
   [c]([X0]) = [0 0][X0] + [2]
   
          [X1]    [1 1][X1]   [0]
   [mark]([X0]) = [0 1][X0] + [0]
   
          [X1]    [1 0][X1]   [2]
   [a__h]([X0]) = [0 1][X0] + [3]
   
       [X1]    [1 0][X1]   [0]
   [d]([X0]) = [0 0][X0] + [2]
   
          [X1]    [1 1][X1]   [1]
   [a__f]([X0]) = [0 1][X0] + [2]
   
       [X1]    [1 0][X1]   [0]
   [g]([X0]) = [0 0][X0] + [1]
   
       [X1]    [1 1][X1]   [0]
   [f]([X0]) = [0 1][X0] + [2]
   
          [X1]    [1 0][X1]   [1]
   [a__c]([X0]) = [0 0][X0] + [2]
   
   
   Qed