YES(?,POLY)

'Pop* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,POLY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  not(true()) -> false()
     , not(false()) -> true()
     , odd(0()) -> false()
     , odd(s(x)) -> not(odd(x))
     , +(x, 0()) -> x
     , +(x, s(y)) -> s(+(x, y))
     , +(s(x), y) -> s(+(x, y))}

Proof Output:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   odd > not, + > not, odd ~ +
  
  and safe mapping
  
   safe(not) = {1}, safe(true) = {}, safe(false) = {}, safe(odd) = {},
   safe(0) = {}, safe(s) = {1}, safe(+) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  not(; true()) -> false()
     , not(; false()) -> true()
     , odd(0();) -> false()
     , odd(s(; x);) -> not(; odd(x;))
     , +(x, 0();) -> x
     , +(x, s(; y);) -> s(; +(x, y;))
     , +(s(; x), y;) -> s(; +(x, y;))}