YES(?,POLY)

'Pop* with parameter subtitution (timeout of 60.0 seconds)'
-----------------------------------------------------------
Answer:           YES(?,POLY)
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:    
  The input was oriented with the instance of POP* as induced by the precedence
  
   find > ite, complete > ite, complete > find, clique > ite,
   clique > find, clique > complete
  
  and safe mapping
  
   safe(ite) = {1, 2, 3}, safe(tt) = {}, safe(ff) = {},
   safe(find) = {1, 2}, safe(nil) = {}, safe(cons) = {1, 2},
   safe(complete) = {1}, safe(clique) = {} .
  
  For your convenience, here is the input in predicative notation:
  
   Rules:
    {  ite(; tt(), u, v) -> u
     , ite(; ff(), u, v) -> v
     , find(nil(); u, v) -> ff()
     , find(cons(; cons(; u, v), E); u, v) -> tt()
     , find(cons(; cons(; u2, v2), E); u, v) -> find(E; u, v)
     , complete(nil(), E; u) -> tt()
     , complete(cons(; v, S), E; u) ->
       ite(; find(E; u, v), complete(S, E; u), ff())
     , clique(nil(), E;) -> tt()
     , clique(cons(; u, K), E;) ->
       ite(; complete(K, E; u), clique(K, E;), ff())}