private static MultiList<Object, Set<Constant>> partitionExchangeable_impl(
      Iterable<DefaultRule> rules) {
    MultiMap<Term, Term> partitioning = new MultiMap<Term, Term>();

    List<Term> constants = Sugar.arrayListFromCollections(constants(rules));
    Set<Term> closed = new HashSet<Term>();

    // checking interchangeability pairwise
    for (int i = 0; i < constants.size(); i++) {
      if (!closed.contains(constants.get(i))) {
        partitioning.put(constants.get(i), constants.get(i));
        for (int j = i + 1; j < constants.size(); j++) {
          if (areExchangeable(constants.get(i), constants.get(j), rules)) {
            partitioning.put(constants.get(i), constants.get(j));
            closed.add(constants.get(j));
          }
        }
      }
    }
    Map<Constant, Constant> map = new HashMap<Constant, Constant>();
    for (Map.Entry<Term, Set<Term>> entry : partitioning.entrySet()) {
      Constant lexmin = null;
      for (Term t : entry.getValue()) {
        if (t instanceof Constant) {
          if (lexmin == null || t.toString().compareTo(lexmin.toString()) < 0) {
            lexmin = (Constant) t;
          }
        }
      }
      for (Term t : entry.getValue()) {
        if (t instanceof Constant) {
          map.put((Constant) t, lexmin);
        }
      }
    }

    MultiMap<Pair<Object, Constant>, Constant> mm =
        new MultiMap<Pair<Object, Constant>, Constant>();
    for (Map.Entry<Constant, Constant> entry : map.entrySet()) {
      mm.put(
          new Pair<Object, Constant>(
              entry.getValue().type() == null ? Sugar.NIL : entry.getValue().type(),
              entry.getValue()),
          entry.getKey());
    }

    MultiList<Object, Set<Constant>> retVal = new MultiList<Object, Set<Constant>>();
    for (Map.Entry<Pair<Object, Constant>, Set<Constant>> entry : mm.entrySet()) {
      retVal.put(entry.getKey().r, entry.getValue());
    }
    return retVal;
  }
 public static Triple<Set<DefaultRule>, Set<Clause>, List<Set<Constant>>> preprocessConstants(
     Collection<DefaultRule> rules,
     Collection<Clause> hardRules,
     List<Set<Constant>> interchangeable) {
   final Map<Term, Term> typedConstants = new HashMap<Term, Term>();
   List<Set<Constant>> retInterchangeable = new ArrayList<Set<Constant>>();
   for (Set<Constant> set : interchangeable) {
     String type = min(set).name();
     Set<Constant> newSet = new HashSet<Constant>();
     for (Constant c : set) {
       Constant typedConstant = Constant.construct(c.name(), type);
       typedConstants.put(c, typedConstant);
       newSet.add(typedConstant);
     }
     retInterchangeable.add(newSet);
   }
   Collection<DefaultRule> retDefaultRules =
       Sugar.funcall(
           rules,
           new Sugar.Fun<DefaultRule, DefaultRule>() {
             @Override
             public DefaultRule apply(DefaultRule defaultRule) {
               return DefaultTransformationUtils.substitute(defaultRule, typedConstants);
             }
           });
   Collection<Clause> retHardRules =
       Sugar.funcall(
           hardRules,
           new Sugar.Fun<Clause, Clause>() {
             @Override
             public Clause apply(Clause hardRule) {
               return LogicUtils.substitute(hardRule, typedConstants);
             }
           });
   return new Triple<Set<DefaultRule>, Set<Clause>, List<Set<Constant>>>(
       Sugar.setFromCollections(retDefaultRules),
       Sugar.setFromCollections(retHardRules),
       Sugar.listFromCollections(retInterchangeable));
 }