YES(?,ELEMENTARY)

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

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