YES(?,ELEMENTARY)

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

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