YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  sum(0()) -> 0()
     , sum(s(x)) -> +(sqr(s(x)), sum(x))
     , sqr(x) -> *(x, x)
     , sum(s(x)) -> +(*(s(x), s(x)), sum(x))}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   sum > sqr
  
  and safe mapping
  
   safe(sum) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {1, 2},
   safe(sqr) = {1}, safe(*) = {1, 2} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  sum(0();) -> 0()
     , sum(s(; x);) -> +(; sqr(; s(; x)), sum(x;))
     , sqr(; x) -> *(; x, x)
     , sum(s(; x);) -> +(; *(; s(; x), s(; x)), sum(x;))}