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)

linear polynomial interpretations on N:

  a__terms_A(x1) = x1 + 7
  a__terms#_A(x1) = x1 + 7
  cons_A(x1,x2) = x1 + 2
  cons#_A(x1,x2) = 4
  recip_A(x1) = x1 + 1
  recip#_A(x1) = 3
  a__sqr_A(x1) = x1 + 4
  a__sqr#_A(x1) = 6
  mark_A(x1) = x1
  mark#_A(x1) = x1 + 3
  terms_A(x1) = x1 + 7
  terms#_A(x1) = 4
  s_A(x1) = 1
  s#_A(x1) = 1
  0_A = 1
  0#_A = 5
  add_A(x1,x2) = x1 + x2 + 2
  add#_A(x1,x2) = 2
  sqr_A(x1) = x1 + 4
  sqr#_A(x1) = 4
  dbl_A(x1) = x1 + 4
  dbl#_A(x1) = 0
  a__dbl_A(x1) = x1 + 4
  a__dbl#_A(x1) = 6
  a__add_A(x1,x2) = x1 + x2 + 2
  a__add#_A(x1,x2) = x2 + 4
  a__first_A(x1,x2) = x1 + x2 + 1
  a__first#_A(x1,x2) = x2 + 3
  nil_A = 1
  nil#_A = 0
  first_A(x1,x2) = x1 + x2 + 1
  first#_A(x1,x2) = 0

precedence:

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