YES

Problem:
 a__g(X) -> a__h(X)
 a__c() -> d()
 a__h(d()) -> a__g(c())
 mark(g(X)) -> a__g(X)
 mark(h(X)) -> a__h(X)
 mark(c()) -> a__c()
 mark(d()) -> d()
 a__g(X) -> g(X)
 a__h(X) -> h(X)
 a__c() -> c()

Proof:
 DP Processor:
  DPs:
   a__g#(X) -> a__h#(X)
   a__h#(d()) -> a__g#(c())
   mark#(g(X)) -> a__g#(X)
   mark#(h(X)) -> a__h#(X)
   mark#(c()) -> a__c#()
  TRS:
   a__g(X) -> a__h(X)
   a__c() -> d()
   a__h(d()) -> a__g(c())
   mark(g(X)) -> a__g(X)
   mark(h(X)) -> a__h(X)
   mark(c()) -> a__c()
   mark(d()) -> d()
   a__g(X) -> g(X)
   a__h(X) -> h(X)
   a__c() -> c()
  TDG Processor:
   DPs:
    a__g#(X) -> a__h#(X)
    a__h#(d()) -> a__g#(c())
    mark#(g(X)) -> a__g#(X)
    mark#(h(X)) -> a__h#(X)
    mark#(c()) -> a__c#()
   TRS:
    a__g(X) -> a__h(X)
    a__c() -> d()
    a__h(d()) -> a__g(c())
    mark(g(X)) -> a__g(X)
    mark(h(X)) -> a__h(X)
    mark(c()) -> a__c()
    mark(d()) -> d()
    a__g(X) -> g(X)
    a__h(X) -> h(X)
    a__c() -> c()
   graph:
    mark#(h(X)) -> a__h#(X) -> a__h#(d()) -> a__g#(c())
    mark#(g(X)) -> a__g#(X) -> a__g#(X) -> a__h#(X)
    a__h#(d()) -> a__g#(c()) -> a__g#(X) -> a__h#(X)
    a__g#(X) -> a__h#(X) -> a__h#(d()) -> a__g#(c())
   SCC Processor:
    #sccs: 1
    #rules: 2
    #arcs: 4/25
    DPs:
     a__h#(d()) -> a__g#(c())
     a__g#(X) -> a__h#(X)
    TRS:
     a__g(X) -> a__h(X)
     a__c() -> d()
     a__h(d()) -> a__g(c())
     mark(g(X)) -> a__g(X)
     mark(h(X)) -> a__h(X)
     mark(c()) -> a__c()
     mark(d()) -> d()
     a__g(X) -> g(X)
     a__h(X) -> h(X)
     a__c() -> c()
    CDG Processor:
     DPs:
      a__h#(d()) -> a__g#(c())
      a__g#(X) -> a__h#(X)
     TRS:
      a__g(X) -> a__h(X)
      a__c() -> d()
      a__h(d()) -> a__g(c())
      mark(g(X)) -> a__g(X)
      mark(h(X)) -> a__h(X)
      mark(c()) -> a__c()
      mark(d()) -> d()
      a__g(X) -> g(X)
      a__h(X) -> h(X)
      a__c() -> c()
     graph:
      a__h#(d()) -> a__g#(c()) -> a__g#(X) -> a__h#(X)
     SCC Processor:
      #sccs: 0
      #rules: 0
      #arcs: 1/4