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

max/plus interpretations on N:

  f_A(x1) = max{11, 4 + x1}
  f#_A(x1) = max{3, 4}
  cons_A(x1,x2) = max{5, 4 + x1, 3 + x2}
  cons#_A(x1,x2) = max{2, 2, 3}
  n__f_A(x1) = max{8, 4 + x1}
  n__f#_A(x1) = max{2, 3}
  n__g_A(x1) = max{4, -3 + x1}
  n__g#_A(x1) = max{4, 2}
  g_A(x1) = max{7, -3 + x1}
  g#_A(x1) = max{1, 5}
  0_A = 1
  0#_A = 4
  s_A(x1) = max{1, -1}
  s#_A(x1) = max{0, 2}
  sel_A(x1,x2) = max{2, 1, -4 + x2}
  sel#_A(x1,x2) = max{11, 12, 5}
  activate_A(x1) = max{6, 3 + x1}
  activate#_A(x1) = max{6, 10}

precedence:

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