YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  f(x, y, w, w, a()) -> g1(x, x, y, w)
     , f(x, y, w, a(), a()) -> g1(y, x, x, w)
     , f(x, y, a(), a(), w) -> g2(x, y, y, w)
     , f(x, y, a(), w, w) -> g2(y, y, x, w)
     , g1(x, x, y, a()) -> h(x, y)
     , g1(y, x, x, a()) -> h(x, y)
     , g2(x, y, y, a()) -> h(x, y)
     , g2(y, y, x, a()) -> h(x, y)
     , h(x, x) -> x}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  f(; x, y, w, w, a()) -> g1(; x, x, y, w)
    , f(; x, y, w, a(), a()) -> g1(; y, x, x, w)
    , f(; x, y, a(), a(), w) -> g2(; x, y, y, w)
    , f(; x, y, a(), w, w) -> g2(; y, y, x, w)
    , g1(; x, x, y, a()) -> h(; x, y)
    , g1(; y, x, x, a()) -> h(; x, y)
    , g2(; x, y, y, a()) -> h(; x, y)
    , g2(; y, y, x, a()) -> h(; x, y)
    , h(; x, x) -> x}
  Safe Mapping:
   safe(f) = {1, 2, 3, 4, 5}, safe(a) = {}, safe(g1) = {1, 2, 3, 4},
   safe(g2) = {1, 2, 3, 4}, safe(h) = {1, 2}
  Argument Permutation:
   mu(f) = [5, 3, 4, 2, 1], mu(g1) = [4, 3, 1, 2],
   mu(g2) = [2, 4, 1, 3], mu(h) = [1, 2]
  Precedence:
   h ~ h, g2 > h, g2 ~ g2, g2 > g1, g1 > h, g1 ~ g1, f > h, f > g2,
   f > g1, f ~ f