TRS:
 {            terms(N) -> cons(recip(sqr(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)) -> cons(Y)}
 RPO Product:
  Quasi-Precedence:
  terms > sqr ~ dbl, 
  sqr ~ dbl > add
  empty
  
  Qed


TRS:
 {            terms(N) -> cons(recip(sqr(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)) -> cons(Y)}
 Cdiprover:
  Interpretation class: quasisimplemixed
  Complexity bound: POLYTIME COMPUTABLE IF RPO-TERMINATING
  first(X9, X8) = + 0*X9^2 + 0*X8^2 + 2*X9 + 2 + 1*X8 + 0*X8*X9
  nil = + 0
  dbl(X7) = + 0*X7^2 + 2 + 2*X7
  add(X6, X5) = + 0*X6^2 + 0*X5^2 + 1*X6 + 0 + 1*X5 + 0*X5*X6
  s(X4) = + 1*X4 + 3
  0 = + 0
  terms(X3) = + 1*X3^2 + 3 + 1*X3
  sqr(X2) = + 1*X2^2 + 0 + 1*X2
  recip(X1) = + 1*X1 + 1
  cons(X0) = + 1*X0 + 2
  
  Qed