YES(?,ELEMENTARY)

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

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