YES
O(n)
TRS:
 {
     a__f(X) -> f(X),
  a__f(g(X)) -> g(X),
      a__c() -> a__f(g(c())),
      a__c() -> c(),
  mark(g(X)) -> g(X),
   mark(c()) -> a__c(),
  mark(f(X)) -> a__f(X)
 }
 Natural interpretation:
  Strict:
   {
       a__f(X) -> f(X),
    a__f(g(X)) -> g(X),
        a__c() -> a__f(g(c())),
        a__c() -> c(),
    mark(g(X)) -> g(X),
     mark(c()) -> a__c(),
    mark(f(X)) -> a__f(X)
   }
  Weak:
   {}
  Interpretation class: stronglylinear
  [f](X0) = + 1*X0 + 0
  [mark](X0) = + 1*X0 + 3
  [a__c] = + 3
  [c] = + 1
  [g](X0) = + 1*X0 + 0
  [a__f](X0) = + 1*X0 + 1
  
  Qed