YES(?,ELEMENTARY)

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

Proof Output:    
  Strict Rules in Predicative Notation:
   {  double(0();) -> 0()
    , double(s(; x);) -> s(; s(; double(x;)))
    , +(x, 0();) -> x
    , +(x, s(; y);) -> s(; +(x, y;))
    , +(s(; x), y;) -> s(; +(x, y;))
    , double(x;) -> +(x, x;)}
  Safe Mapping:
   safe(double) = {}, safe(0) = {}, safe(s) = {1}, safe(+) = {}
  Argument Permutation:
   mu(double) = [1], mu(+) = [2, 1]
  Precedence:
   + ~ +, double > +, double ~ double