YES
O(n)
TRS:
 {
     a__h(X) -> h(X),
   a__h(d()) -> a__g(c()),
     a__g(X) -> a__h(X),
     a__g(X) -> g(X),
      a__c() -> d(),
      a__c() -> c(),
   mark(d()) -> d(),
   mark(c()) -> a__c(),
  mark(g(X)) -> a__g(X),
  mark(h(X)) -> a__h(X)
 }
 Natural interpretation:
  Strict:
   {
       a__h(X) -> h(X),
     a__h(d()) -> a__g(c()),
       a__g(X) -> a__h(X),
       a__g(X) -> g(X),
        a__c() -> d(),
        a__c() -> c(),
     mark(d()) -> d(),
     mark(c()) -> a__c(),
    mark(g(X)) -> a__g(X),
    mark(h(X)) -> a__h(X)
   }
  Weak:
   {}
  Interpretation class: stronglylinear
  [h](X0) = + 1*X0 + 0
  [g](X0) = + 1*X0 + 0
  [mark](X0) = + 1*X0 + 6
  [c] = + 0
  [a__c] = + 4
  [d] = + 2
  [a__g](X0) = + 1*X0 + 5
  [a__h](X0) = + 1*X0 + 4
  
  Qed