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{19, 14 + x1}
  terms#_A(x1) = max{19, 14 + x1}
  cons_A(x1,x2) = max{2, 6 + x1, x2}
  cons#_A(x1,x2) = max{2, 6 + x1, x2}
  recip_A(x1) = max{13, x1}
  recip#_A(x1) = max{13, x1}
  sqr_A(x1) = max{13, 7 + x1}
  sqr#_A(x1) = max{13, 7 + x1}
  n__terms_A(x1) = max{19, 14 + x1}
  n__terms#_A(x1) = max{19, 14 + x1}
  n__s_A(x1) = max{5, x1}
  n__s#_A(x1) = max{5, x1}
  0_A = 3
  0#_A = 3
  s_A(x1) = max{5, x1}
  s#_A(x1) = max{5, x1}
  add_A(x1,x2) = max{6, x1, 5 + x2}
  add#_A(x1,x2) = max{6, x1, 5 + x2}
  dbl_A(x1) = max{4, 1 + x1}
  dbl#_A(x1) = max{4, 1 + x1}
  first_A(x1,x2) = max{14, 8 + x1, 3 + x2}
  first#_A(x1,x2) = max{14, 8 + x1, 3 + x2}
  nil_A = 2
  nil#_A = 2
  n__first_A(x1,x2) = max{14, 8 + x1, 3 + x2}
  n__first#_A(x1,x2) = max{14, 8 + x1, 3 + x2}
  activate_A(x1) = max{4, x1}
  activate#_A(x1) = max{4, x1}
  half_A(x1) = max{6, 1 + x1}
  half#_A(x1) = max{6, 1 + x1}

precedence:

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