YES

TRS:

  f(X) -> cons(X,n__f(g(X)))
  g(0()) -> s(0())
  g(s(X)) -> s(s(g(X)))
  sel(0(),cons(X,Y)) -> X
  sel(s(X),cons(Y,Z)) -> sel(X,activate(Z))
  f(X) -> n__f(X)
  activate(n__f(X)) -> f(X)
  activate(X) -> X

max/plus interpretations on N:

  f_A(x1) = max{3, 2 + x1}
  f#_A(x1) = max{4, 1}
  cons_A(x1,x2) = max{2, 2 + x1, 1 + x2}
  cons#_A(x1,x2) = max{0, 2, 2}
  n__f_A(x1) = max{1, 1 + x1}
  n__f#_A(x1) = max{0, 2}
  g_A(x1) = max{1, -4 + x1}
  g#_A(x1) = max{2, 4}
  0_A = 1
  0#_A = 3
  s_A(x1) = max{0, -2}
  s#_A(x1) = max{3, 1}
  sel_A(x1,x2) = max{3, 0, x2}
  sel#_A(x1,x2) = max{6, 8, 7}
  activate_A(x1) = max{3, 1 + x1}
  activate#_A(x1) = max{3, 5}

precedence:

  cons = sel > activate > f > n__f = g > 0 = s