YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  terms(N) -> cons(recip(sqr(N)))
     , sqr(0()) -> 0()
     , sqr(s()) -> s()
     , dbl(0()) -> 0()
     , dbl(s()) -> s()
     , add(0(), X) -> X
     , add(s(), Y) -> s()
     , first(0(), X) -> nil()
     , first(s(), cons(Y)) -> cons(Y)}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  terms(N;) -> cons(; recip(; sqr(N;)))
    , sqr(0();) -> 0()
    , sqr(s();) -> s()
    , dbl(; 0()) -> 0()
    , dbl(; s()) -> s()
    , add(; 0(), X) -> X
    , add(; s(), Y) -> s()
    , first(X; 0()) -> nil()
    , first(cons(; Y); s()) -> cons(; Y)}
  Safe Mapping:
   safe(terms) = {}, safe(cons) = {1}, safe(recip) = {1},
   safe(sqr) = {}, safe(0) = {}, safe(s) = {}, safe(dbl) = {1},
   safe(add) = {1, 2}, safe(first) = {1}, safe(nil) = {}
  Argument Permutation:
   mu(terms) = [1], mu(sqr) = [1], mu(dbl) = [1], mu(add) = [2, 1],
   mu(first) = [2, 1]
  Precedence:
   first ~ first, first ~ sqr, add > first, add ~ add, add > dbl,
   add > sqr, add > terms, dbl > first, dbl ~ dbl, dbl > sqr,
   sqr ~ first, sqr ~ sqr, terms > first, terms > dbl, terms > sqr,
   terms ~ terms