YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
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:    
  Strict Rules in Predicative Notation:
   {  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;))}
  Safe Mapping:
   safe(not) = {1}, safe(true) = {}, safe(false) = {}, safe(odd) = {},
   safe(0) = {}, safe(s) = {1}, safe(+) = {}
  Argument Permutation:
   mu(not) = [1], mu(odd) = [1], mu(+) = [2, 1]
  Precedence:
   + ~ +, + > odd, + > not, odd ~ odd, odd > not, not ~ not