YES

TRS:

  terms(N) -> cons(recip(sqr(N)))
  sqr(0()) -> 0()
  sqr(s()) -> s()
  dbl(0()) -> 0()
  dbl(s()) -> s()
  add(0(),X) -> X
  add(s(),Y) -> s()
  first(0(),X) -> nil()
  first(s(),cons(Y)) -> cons(Y)

linear polynomial interpretations on N:

  terms_A(x1) = x1 + 2
  terms#_A(x1) = x1 + 2
  cons_A(x1) = x1
  cons#_A(x1) = x1
  recip_A(x1) = x1
  recip#_A(x1) = x1
  sqr_A(x1) = x1 + 1
  sqr#_A(x1) = x1 + 1
  0_A = 1
  0#_A = 1
  s_A = 1
  s#_A = 1
  dbl_A(x1) = x1 + 1
  dbl#_A(x1) = x1 + 1
  add_A(x1,x2) = x1 + x2 + 1
  add#_A(x1,x2) = x1 + x2 + 1
  first_A(x1,x2) = x1 + x2
  first#_A(x1,x2) = x1 + x2
  nil_A = 0
  nil#_A = 0

precedence:

  0 > nil > terms = s = first > cons = recip = sqr = dbl = add