YES

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)

linear polynomial interpretations on N:

  a__f_A(x1) = 1
  a__f#_A(x1) = x1 + 2
  0_A = 1
  0#_A = 2
  cons_A(x1,x2) = 1
  cons#_A(x1,x2) = 2
  f_A(x1) = 1
  f#_A(x1) = 1
  s_A(x1) = 2
  s#_A(x1) = 1
  a__p_A(x1) = 1
  a__p#_A(x1) = 1
  mark_A(x1) = 2
  mark#_A(x1) = 5
  p_A(x1) = 1
  p#_A(x1) = 0

precedence:

  f = a__p > a__f = p > cons = s > mark > 0