YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
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:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   terms > sqr, terms > dbl, terms > first, add > sqr, add > dbl,
   add > first, terms ~ add, sqr ~ dbl, sqr ~ first, dbl ~ first
  
  and safe mapping
  
   safe(terms) = {}, safe(cons) = {1}, safe(recip) = {1},
   safe(sqr) = {1}, safe(0) = {}, safe(s) = {}, safe(dbl) = {},
   safe(add) = {}, safe(first) = {1}, safe(nil) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   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(X; 0()) -> nil()
     , first(cons(; Y); s()) -> cons(; Y)}