YES

Problem:
 a__f(f(a())) -> c(f(g(f(a()))))
 mark(f(X)) -> a__f(mark(X))
 mark(a()) -> a()
 mark(c(X)) -> c(X)
 mark(g(X)) -> g(mark(X))
 a__f(X) -> f(X)

Proof:
 DP Processor:
  DPs:
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(g(X)) -> mark#(X)
  TRS:
   a__f(f(a())) -> c(f(g(f(a()))))
   mark(f(X)) -> a__f(mark(X))
   mark(a()) -> a()
   mark(c(X)) -> c(X)
   mark(g(X)) -> g(mark(X))
   a__f(X) -> f(X)
  TDG Processor:
   DPs:
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X))
    mark#(g(X)) -> mark#(X)
   TRS:
    a__f(f(a())) -> c(f(g(f(a()))))
    mark(f(X)) -> a__f(mark(X))
    mark(a()) -> a()
    mark(c(X)) -> c(X)
    mark(g(X)) -> g(mark(X))
    a__f(X) -> f(X)
   graph:
    mark#(g(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(g(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(g(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(g(X)) -> mark#(X)
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> a__f#(mark(X))
    mark#(f(X)) -> mark#(X) -> mark#(f(X)) -> mark#(X)
   CDG Processor:
    DPs:
     mark#(f(X)) -> mark#(X)
     mark#(f(X)) -> a__f#(mark(X))
     mark#(g(X)) -> mark#(X)
    TRS:
     a__f(f(a())) -> c(f(g(f(a()))))
     mark(f(X)) -> a__f(mark(X))
     mark(a()) -> a()
     mark(c(X)) -> c(X)
     mark(g(X)) -> g(mark(X))
     a__f(X) -> f(X)
    graph:
     
    Qed