YES
TRS:
 {     a__f(X) -> f(X),
  a__f(f(a())) -> a__f(g(f(a()))),
    mark(g(X)) -> g(X),
    mark(f(X)) -> a__f(mark(X)),
     mark(a()) -> a()}
 DP:
  Strict:
   {a__f#(f(a())) -> a__f#(g(f(a()))),
      mark#(f(X)) -> a__f#(mark(X)),
      mark#(f(X)) -> mark#(X)}
  Weak:
  {     a__f(X) -> f(X),
   a__f(f(a())) -> a__f(g(f(a()))),
     mark(g(X)) -> g(X),
     mark(f(X)) -> a__f(mark(X)),
      mark(a()) -> a()}
  EDG:
   {(mark#(f(X)) -> a__f#(mark(X)), a__f#(f(a())) -> a__f#(g(f(a()))))
    (mark#(f(X)) -> mark#(X), mark#(f(X)) -> a__f#(mark(X)))
    (mark#(f(X)) -> mark#(X), mark#(f(X)) -> mark#(X))}
   SCCS:
    Scc:
     {mark#(f(X)) -> mark#(X)}
    SCC:
     Strict:
      {mark#(f(X)) -> mark#(X)}
     Weak:
     {     a__f(X) -> f(X),
      a__f(f(a())) -> a__f(g(f(a()))),
        mark(g(X)) -> g(X),
        mark(f(X)) -> a__f(mark(X)),
         mark(a()) -> a()}
     SPSC:
      Simple Projection:
       pi(mark#) = 0
      Strict:
       {}
      Qed