YES

Problem:
 a__f(0()) -> cons(0(),f(s(0())))
 a__f(s(0())) -> a__f(a__p(s(0())))
 a__p(s(0())) -> 0()
 mark(f(X)) -> a__f(mark(X))
 mark(p(X)) -> a__p(mark(X))
 mark(0()) -> 0()
 mark(cons(X1,X2)) -> cons(mark(X1),X2)
 mark(s(X)) -> s(mark(X))
 a__f(X) -> f(X)
 a__p(X) -> p(X)

Proof:
 DP Processor:
  DPs:
   a__f#(s(0())) -> a__p#(s(0()))
   a__f#(s(0())) -> a__f#(a__p(s(0())))
   mark#(f(X)) -> mark#(X)
   mark#(f(X)) -> a__f#(mark(X))
   mark#(p(X)) -> mark#(X)
   mark#(p(X)) -> a__p#(mark(X))
   mark#(cons(X1,X2)) -> mark#(X1)
   mark#(s(X)) -> mark#(X)
  TRS:
   a__f(0()) -> cons(0(),f(s(0())))
   a__f(s(0())) -> a__f(a__p(s(0())))
   a__p(s(0())) -> 0()
   mark(f(X)) -> a__f(mark(X))
   mark(p(X)) -> a__p(mark(X))
   mark(0()) -> 0()
   mark(cons(X1,X2)) -> cons(mark(X1),X2)
   mark(s(X)) -> s(mark(X))
   a__f(X) -> f(X)
   a__p(X) -> p(X)
  CDG Processor:
   DPs:
    a__f#(s(0())) -> a__p#(s(0()))
    a__f#(s(0())) -> a__f#(a__p(s(0())))
    mark#(f(X)) -> mark#(X)
    mark#(f(X)) -> a__f#(mark(X))
    mark#(p(X)) -> mark#(X)
    mark#(p(X)) -> a__p#(mark(X))
    mark#(cons(X1,X2)) -> mark#(X1)
    mark#(s(X)) -> mark#(X)
   TRS:
    a__f(0()) -> cons(0(),f(s(0())))
    a__f(s(0())) -> a__f(a__p(s(0())))
    a__p(s(0())) -> 0()
    mark(f(X)) -> a__f(mark(X))
    mark(p(X)) -> a__p(mark(X))
    mark(0()) -> 0()
    mark(cons(X1,X2)) -> cons(mark(X1),X2)
    mark(s(X)) -> s(mark(X))
    a__f(X) -> f(X)
    a__p(X) -> p(X)
   graph:
    
   Qed