YES

TRS:

  terms(N) -> cons(recip(sqr(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)) -> cons(Y)
  half(0()) -> 0()
  half(s(0())) -> 0()
  half(s(s(X))) -> s(half(X))
  half(dbl(X)) -> X

linear polynomial interpretations on N:

  terms_A(x1) = x1 + 2
  terms#_A(x1) = x1 + 5
  cons_A(x1) = x1 + 1
  cons#_A(x1) = x1
  recip_A(x1) = x1
  recip#_A(x1) = x1 + 3
  sqr_A(x1) = x1 + 1
  sqr#_A(x1) = 4
  0_A = 1
  0#_A = 1
  s_A(x1) = 1
  s#_A(x1) = 2
  add_A(x1,x2) = x2 + 1
  add#_A(x1,x2) = 3
  dbl_A(x1) = x1 + 1
  dbl#_A(x1) = 3
  first_A(x1,x2) = x2
  first#_A(x1,x2) = x2 + 1
  nil_A = 0
  nil#_A = 0
  half_A(x1) = x1 + 2
  half#_A(x1) = 0

precedence:

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