YES(?,ELEMENTARY)

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

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