YES

TRS:

  terms(N) -> cons(recip(sqr(N)),n__terms(n__s(N)))
  sqr(0()) -> 0()
  sqr(s(X)) -> s(add(sqr(X),dbl(X)))
  dbl(0()) -> 0()
  dbl(s(X)) -> s(s(dbl(X)))
  add(0(),X) -> X
  add(s(X),Y) -> s(add(X,Y))
  first(0(),X) -> nil()
  first(s(X),cons(Y,Z)) -> cons(Y,n__first(X,activate(Z)))
  half(0()) -> 0()
  half(s(0())) -> 0()
  half(s(s(X))) -> s(half(X))
  half(dbl(X)) -> X
  terms(X) -> n__terms(X)
  s(X) -> n__s(X)
  first(X1,X2) -> n__first(X1,X2)
  activate(n__terms(X)) -> terms(activate(X))
  activate(n__s(X)) -> s(activate(X))
  activate(n__first(X1,X2)) -> first(activate(X1),activate(X2))
  activate(X) -> X

max/plus interpretations on N:

  terms_A(x1) = max{48, 20 + x1}
  terms#_A(x1) = max{20, 21 + x1}
  cons_A(x1,x2) = max{27, 47 + x1, -4 + x2}
  cons#_A(x1,x2) = max{13, 1, 10}
  recip_A(x1) = max{1, -25 + x1}
  recip#_A(x1) = max{21, -5 + x1}
  sqr_A(x1) = max{26, -2 + x1}
  sqr#_A(x1) = max{17, 19}
  n__terms_A(x1) = max{48, 20 + x1}
  n__terms#_A(x1) = max{10, 1}
  n__s_A(x1) = max{5, x1}
  n__s#_A(x1) = max{1, 3}
  0_A = 8
  0#_A = 8
  s_A(x1) = max{5, x1}
  s#_A(x1) = max{0, 10}
  add_A(x1,x2) = max{5, 4, x2}
  add#_A(x1,x2) = max{16, 11, 16}
  dbl_A(x1) = max{8, -2 + x1}
  dbl#_A(x1) = max{16, 18}
  first_A(x1,x2) = max{26, 17 + x1, 19 + x2}
  first#_A(x1,x2) = max{10, 3 + x1, 16 + x2}
  nil_A = 26
  nil#_A = 7
  n__first_A(x1,x2) = max{26, 17 + x1, 19 + x2}
  n__first#_A(x1,x2) = max{9, 2 + x1, 11}
  activate_A(x1) = max{2, x1}
  activate#_A(x1) = max{11, 2 + x1}
  half_A(x1) = max{0, 2 + x1}
  half#_A(x1) = max{7, 9}

precedence:

  cons = n__first > activate > terms = s = first > recip = sqr = n__terms = n__s = half > add = dbl > 0 > nil