YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(0()) -> 1()
     , f(s(x)) -> g(f(x))
     , g(x) -> +(x, s(x))
     , f(s(x)) -> +(f(x), s(f(x)))}

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