YES

TRS:

  from(X) -> cons(X,n__from(s(X)))
  2ndspos(0(),Z) -> rnil()
  2ndspos(s(N),cons(X,n__cons(Y,Z))) -> rcons(posrecip(activate(Y)),2ndsneg(N,activate(Z)))
  2ndsneg(0(),Z) -> rnil()
  2ndsneg(s(N),cons(X,n__cons(Y,Z))) -> rcons(negrecip(activate(Y)),2ndspos(N,activate(Z)))
  pi(X) -> 2ndspos(X,from(0()))
  plus(0(),Y) -> Y
  plus(s(X),Y) -> s(plus(X,Y))
  times(0(),Y) -> 0()
  times(s(X),Y) -> plus(Y,times(X,Y))
  square(X) -> times(X,X)
  from(X) -> n__from(X)
  cons(X1,X2) -> n__cons(X1,X2)
  activate(n__from(X)) -> from(X)
  activate(n__cons(X1,X2)) -> cons(X1,X2)
  activate(X) -> X

linear polynomial interpretations on N:

  from_A(x1) = x1 + 4
  from#_A(x1) = 2
  cons_A(x1,x2) = x1 + x2 + 4
  cons#_A(x1,x2) = x2 + 1
  n__from_A(x1) = x1
  n__from#_A(x1) = 1
  s_A(x1) = 0
  s#_A(x1) = 0
  2ndspos_A(x1,x2) = x1 + 1
  2ndspos#_A(x1,x2) = 4
  0_A = 1
  0#_A = 1
  rnil_A = 0
  rnil#_A = 0
  n__cons_A(x1,x2) = x1 + x2 + 4
  n__cons#_A(x1,x2) = x2
  rcons_A(x1,x2) = x1
  rcons#_A(x1,x2) = 0
  posrecip_A(x1) = 1
  posrecip#_A(x1) = 4
  activate_A(x1) = x1 + 4
  activate#_A(x1) = x1 + 3
  2ndsneg_A(x1,x2) = x1 + x2
  2ndsneg#_A(x1,x2) = 4
  negrecip_A(x1) = 1
  negrecip#_A(x1) = 4
  pi_A(x1) = x1 + 1
  pi#_A(x1) = x1 + 5
  plus_A(x1,x2) = x2
  plus#_A(x1,x2) = 1
  times_A(x1,x2) = 1
  times#_A(x1,x2) = x2 + 2
  square_A(x1) = 1
  square#_A(x1) = x1 + 3

precedence:

  cons = pi = times = square > 2ndspos = 0 = n__cons = 2ndsneg = plus > n__from = rnil = rcons = posrecip = activate = negrecip > from > s