YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  admit(x, nil()) -> nil()
     , admit(x, .(u, .(v, .(w(), z)))) ->
       cond(=(sum(x, u, v), w()),
            .(u, .(v, .(w(), admit(carry(x, u, v), z)))))
     , cond(true(), y) -> y}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  admit(nil(); x) -> nil()
    , admit(.(; u, .(; v, .(; w(), z))); x) ->
      cond(; =(; sum(; x, u, v), w()),
             .(; u, .(; v, .(; w(), admit(z; carry(; x, u, v))))))
    , cond(; true(), y) -> y}
  Safe Mapping:
   safe(admit) = {1}, safe(nil) = {}, safe(.) = {1, 2}, safe(w) = {},
   safe(cond) = {1, 2}, safe(=) = {1, 2}, safe(sum) = {1, 2, 3},
   safe(carry) = {1, 2, 3}, safe(true) = {}
  Argument Permutation:
   mu(admit) = [2, 1], mu(cond) = [2, 1]
  Precedence:
   cond ~ cond, admit > cond, admit ~ admit