YES(?,POLY)

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

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