YES(?,ELEMENTARY)

'epo* (timeout of 60.0 seconds)'
--------------------------------
Answer:           YES(?,ELEMENTARY)
Input Problem:    innermost runtime-complexity with respect to
  Rules:
    {  ite(tt(), u, v) -> u
     , ite(ff(), u, v) -> v
     , find(u, v, nil()) -> ff()
     , find(u, v, cons(cons(u, v), E)) -> tt()
     , find(u, v, cons(cons(u2, v2), E)) -> find(u, v, E)
     , complete(u, nil(), E) -> tt()
     , complete(u, cons(v, S), E) ->
       ite(find(u, v, E), complete(u, S, E), ff())
     , clique(nil(), E) -> tt()
     , clique(cons(u, K), E) ->
       ite(complete(u, K, E), clique(K, E), ff())}

Proof Output:    
  Strict Rules in Predicative Notation:
   {  ite(; tt(), u, v) -> u
    , ite(; ff(), u, v) -> v
    , find(u, v, nil();) -> ff()
    , find(u, v, cons(; cons(; u, v), E);) -> tt()
    , find(u, v, cons(; cons(; u2, v2), E);) -> find(u, v, E;)
    , complete(u, nil(), E;) -> tt()
    , complete(u, cons(; v, S), E;) ->
      ite(; find(u, v, E;), complete(u, S, E;), ff())
    , clique(nil(), E;) -> tt()
    , clique(cons(; u, K), E;) ->
      ite(; complete(u, K, E;), clique(K, E;), ff())}
  Safe Mapping:
   safe(ite) = {1, 2, 3}, safe(tt) = {}, safe(ff) = {},
   safe(find) = {}, safe(nil) = {}, safe(cons) = {1, 2},
   safe(complete) = {}, safe(clique) = {}
  Argument Permutation:
   mu(ite) = [2, 1, 3], mu(find) = [2, 3, 1],
   mu(complete) = [2, 3, 1], mu(clique) = [1, 2]
  Precedence:
   clique ~ clique, clique > complete, clique > find, clique > ite,
   complete ~ complete, complete > find, complete > ite, find ~ find,
   find > ite, ite ~ ite