YES

TRS:

  a__terms(N) -> cons(recip(a__sqr(mark(N))),terms(s(N)))
  a__sqr(0()) -> 0()
  a__sqr(s(X)) -> s(add(sqr(X),dbl(X)))
  a__dbl(0()) -> 0()
  a__dbl(s(X)) -> s(s(dbl(X)))
  a__add(0(),X) -> mark(X)
  a__add(s(X),Y) -> s(add(X,Y))
  a__first(0(),X) -> nil()
  a__first(s(X),cons(Y,Z)) -> cons(mark(Y),first(X,Z))
  mark(terms(X)) -> a__terms(mark(X))
  mark(sqr(X)) -> a__sqr(mark(X))
  mark(add(X1,X2)) -> a__add(mark(X1),mark(X2))
  mark(dbl(X)) -> a__dbl(mark(X))
  mark(first(X1,X2)) -> a__first(mark(X1),mark(X2))
  mark(cons(X1,X2)) -> cons(mark(X1),X2)
  mark(recip(X)) -> recip(mark(X))
  mark(s(X)) -> s(X)
  mark(0()) -> 0()
  mark(nil()) -> nil()
  a__terms(X) -> terms(X)
  a__sqr(X) -> sqr(X)
  a__add(X1,X2) -> add(X1,X2)
  a__dbl(X) -> dbl(X)
  a__first(X1,X2) -> first(X1,X2)

max/plus interpretations on N:

  a__terms_A(x1) = max{39, 101 + x1}
  a__terms#_A(x1) = max{49, 33 + x1}
  cons_A(x1,x2) = max{39, 39 + x1, 39}
  cons#_A(x1,x2) = max{49, 30, 49}
  recip_A(x1) = max{18, 21 + x1}
  recip#_A(x1) = max{34, 49}
  a__sqr_A(x1) = max{18, 22 + x1}
  a__sqr#_A(x1) = max{45, 34}
  mark_A(x1) = max{17, 19 + x1}
  mark#_A(x1) = max{46, 32 + x1}
  terms_A(x1) = max{16, 101 + x1}
  terms#_A(x1) = max{31, 0}
  s_A(x1) = max{0, -23}
  s#_A(x1) = max{38, 37}
  0_A = 22
  0#_A = 35
  add_A(x1,x2) = max{28, 12 + x1, 27 + x2}
  add#_A(x1,x2) = max{0, 44, 40}
  sqr_A(x1) = max{19, 22 + x1}
  sqr#_A(x1) = max{45, 34}
  dbl_A(x1) = max{25, 24 + x1}
  dbl#_A(x1) = max{45, 31}
  a__dbl_A(x1) = max{44, 24 + x1}
  a__dbl#_A(x1) = max{47, 36}
  a__add_A(x1,x2) = max{47, 12 + x1, 27 + x2}
  a__add#_A(x1,x2) = max{45, 24 + x1, 39 + x2}
  a__first_A(x1,x2) = max{42, 22 + x1, 19 + x2}
  a__first#_A(x1,x2) = max{49, 31 + x1, 10 + x2}
  nil_A = 43
  nil#_A = 53
  first_A(x1,x2) = max{23, 22 + x1, 19 + x2}
  first#_A(x1,x2) = max{30, 47, 49}

precedence:

  terms > a__terms = add > a__sqr = a__first > cons = sqr = a__add = first > mark > recip = a__dbl > 0 = dbl > s = nil