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)

max/plus interpretations on N:

  a__f_A(x1) = max{1, 10}
  a__f#_A(x1) = max{10, 5 + x1}
  0_A = 1
  0#_A = 26
  cons_A(x1,x2) = max{1, -1, -1}
  cons#_A(x1,x2) = max{7, 8, 9}
  f_A(x1) = max{10, 10}
  f#_A(x1) = max{10, 10}
  s_A(x1) = max{6, 9}
  s#_A(x1) = max{10, 10}
  a__p_A(x1) = max{4, -4}
  a__p#_A(x1) = max{1, 3 + x1}
  mark_A(x1) = max{10, -4}
  mark#_A(x1) = max{25, 16}
  p_A(x1) = max{4, -1}
  p#_A(x1) = max{0, 2 + x1}

precedence:

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