YES

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

Proof:
 DP Processor:
  DPs:
   a__f#(f(X)) -> a__c#(f(g(f(X))))
   a__h#(X) -> a__c#(d(X))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(c(X)) -> a__c#(X)
   mark#(h(X)) -> mark#(X)
   mark#(h(X)) -> a__h#(mark(X))
  TRS:
   a__f(f(X)) -> a__c(f(g(f(X))))
   a__c(X) -> d(X)
   a__h(X) -> a__c(d(X))
   mark(f(X)) -> a__f(mark(X))
   mark(c(X)) -> a__c(X)
   mark(h(X)) -> a__h(mark(X))
   mark(g(X)) -> g(X)
   mark(d(X)) -> d(X)
   a__f(X) -> f(X)
   a__c(X) -> c(X)
   a__h(X) -> h(X)
  TDG Processor:
   DPs:
    a__f#(f(X)) -> a__c#(f(g(f(X))))
    a__h#(X) -> a__c#(d(X))
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X))
    mark#(c(X)) -> a__c#(X)
    mark#(h(X)) -> mark#(X)
    mark#(h(X)) -> a__h#(mark(X))
   TRS:
    a__f(f(X)) -> a__c(f(g(f(X))))
    a__c(X) -> d(X)
    a__h(X) -> a__c(d(X))
    mark(f(X)) -> a__f(mark(X))
    mark(c(X)) -> a__c(X)
    mark(h(X)) -> a__h(mark(X))
    mark(g(X)) -> g(X)
    mark(d(X)) -> d(X)
    a__f(X) -> f(X)
    a__c(X) -> c(X)
    a__h(X) -> h(X)
   graph:
    mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> a__h#(mark(X))
    mark#(h(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X)
    mark#(h(X)) -> mark#(X) -> mark#(c(X)) -> a__c#(X)
    mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(h(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(h(X)) -> a__h#(mark(X)) -> a__h#(X) -> a__c#(d(X))
    mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> a__h#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(h(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(c(X)) -> a__c#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X)) -> a__f#(f(X)) -> a__c#(f(g(f(X))))
   CDG Processor:
    DPs:
     a__f#(f(X)) -> a__c#(f(g(f(X))))
     a__h#(X) -> a__c#(d(X))
     mark#(f(X)) -> mark#(X)
     mark#(f(X)) -> a__f#(mark(X))
     mark#(c(X)) -> a__c#(X)
     mark#(h(X)) -> mark#(X)
     mark#(h(X)) -> a__h#(mark(X))
    TRS:
     a__f(f(X)) -> a__c(f(g(f(X))))
     a__c(X) -> d(X)
     a__h(X) -> a__c(d(X))
     mark(f(X)) -> a__f(mark(X))
     mark(c(X)) -> a__c(X)
     mark(h(X)) -> a__h(mark(X))
     mark(g(X)) -> g(X)
     mark(d(X)) -> d(X)
     a__f(X) -> f(X)
     a__c(X) -> c(X)
     a__h(X) -> h(X)
    graph:
     mark#(h(X)) -> a__h#(mark(X)) -> a__h#(X) -> a__c#(d(X))
     mark#(f(X)) -> a__f#(mark(X)) -> a__f#(f(X)) -> a__c#(f(g(f(X))))
    SCC Processor:
     #sccs: 0
     #rules: 0
     #arcs: 2/49