YES

TRS:

  f(X) -> cons(X,n__f(n__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)
  g(X) -> n__g(X)
  activate(n__f(X)) -> f(activate(X))
  activate(n__g(X)) -> g(activate(X))
  activate(X) -> X

linear polynomial interpretations on N:

  f_A(x1) = x1 + 1
  f#_A(x1) = 1
  cons_A(x1,x2) = x1 + x2
  cons#_A(x1,x2) = 0
  n__f_A(x1) = x1 + 1
  n__f#_A(x1) = 0
  n__g_A(x1) = 0
  n__g#_A(x1) = 0
  g_A(x1) = 0
  g#_A(x1) = 1
  0_A = 1
  0#_A = 0
  s_A(x1) = 0
  s#_A(x1) = 0
  sel_A(x1,x2) = x2
  sel#_A(x1,x2) = 3
  activate_A(x1) = x1
  activate#_A(x1) = 2

precedence:

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