YES(?,ELEMENTARY)

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

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