YES(?,POLY)

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

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