Input TRS:
    1: terms(N) -> cons(recip(sqr(N)))
    2: sqr(0()) -> 0()
    3: sqr(s()) -> s()
    4: dbl(0()) -> 0()
    5: dbl(s()) -> s()
    6: add(0(),X) -> X
    7: add(s(),Y) -> s()
    8: first(0(),X) -> nil()
    9: first(s(),cons(Y)) -> cons(Y)
Number of strict rules: 9
Direct Order(PosReal,>,Poly) ... removes: 4 8 1 3 5 7 9 6 2
     s()	weight: 0
 recip(x1)	weight: 8365 + x1
   dbl(x1)	weight: (/ 1 4) + x1
     0()	weight: 0
   nil()	weight: 0
 first(x1,x2)	weight: (/ 1 4) + x1 + 2 * x2
  cons(x1)	weight: (/ 1 4) + 2 * x1
   add(x1,x2)	weight: (/ 1 4) + x1 + x2
   sqr(x1)	weight: (/ 1 4) + x1
 terms(x1)	weight: 16731 + 2 * x1
Number of strict rules: 0
YES