YES(?,O(n^1))
TRS:
 {
    a__h X -> h X,
  a__h d() -> a__g c(),
    a__g X -> g X,
    a__g X -> a__h X,
    a__c() -> d(),
    a__c() -> c(),
  mark g X -> a__g X,
  mark h X -> a__h X,
  mark d() -> d(),
  mark c() -> a__c()
 }
 DUP: We consider a non-duplicating system.
  Trs:
   {
      a__h X -> h X,
    a__h d() -> a__g c(),
      a__g X -> g X,
      a__g X -> a__h X,
      a__c() -> d(),
      a__c() -> c(),
    mark g X -> a__g X,
    mark h X -> a__h X,
    mark d() -> d(),
    mark c() -> a__c()
   }
  Natural interpretation:
   Strict:
    {
       a__h X -> h X,
     a__h d() -> a__g c(),
       a__g X -> g X,
       a__g X -> a__h X,
       a__c() -> d(),
       a__c() -> c(),
     mark g X -> a__g X,
     mark h X -> a__h X,
     mark d() -> d(),
     mark c() -> a__c()
    }
   Weak:
    {}
   Interpretation class: stronglylinear
   [mark](X0) = + 1*X0 + 7
   [c] = + 1
   [a__c] = + 7
   [d] = + 4
   [a__g](X0) = + 1*X0 + 5
   [a__h](X0) = + 1*X0 + 4
   [h](X0) = + 1*X0 + 0
   [g](X0) = + 1*X0 + 0
   
   Qed