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