diff --git a/lib/mealy.hpp b/lib/mealy.hpp
index f587251..4f17dfb 100644
--- a/lib/mealy.hpp
+++ b/lib/mealy.hpp
@@ -37,3 +37,17 @@ inline auto is_complete(const Mealy & m){
 	}
 	return true;
 }
+
+inline auto apply(Mealy const & m, size_t state, size_t input){
+	return m.graph[state][input];
+}
+
+template <typename Iterator>
+auto apply(Mealy const & m, size_t state, Iterator b, Iterator e){
+	Mealy::edge ret;
+	while(b != e){
+		ret = apply(m, state, *b++);
+		state = ret.to;
+	}
+	return ret;
+}
diff --git a/src/main.cpp b/src/main.cpp
index 1e715e9..56aa31e 100644
--- a/src/main.cpp
+++ b/src/main.cpp
@@ -1,38 +1,58 @@
-#include <partition.hpp>
 #include <mealy.hpp>
+#include <partition.hpp>
 #include <read_mealy_from_dot.hpp>
 
 #include <cassert>
+#include <numeric>
 #include <queue>
-#include <vector>
 #include <type_traits>
+#include <vector>
 
 using namespace std;
 
 int verbose = 0;
 
-// TODO: I was working on this...
-// I didn't know how to do lca for this case...
 struct splijtboom {
+	splijtboom(size_t N)
+	: states(N)
+	{
+		iota(begin(states), end(states), 0);
+	}
+
 	vector<size_t> states;
 	vector<splijtboom> children;
-
-	const splijtboom * parent = nullptr;
+	vector<size_t> seperator;
+	int mark = 0;
 };
 
 template <typename Fun>
-bool lca_impl(const splijtboom & node, Fun && f){
-	int count = 0;
-	for(auto && c : node.children){
-		if(lca_impl(c, f)) count++;
+void lca_impl1(splijtboom & node, Fun && f){
+	node.mark = 0;
+	if(!node.children.empty()){
+		for(auto && c : node.children){
+			lca_impl1(c, f);
+			if(c.mark) node.mark++;
+		}
+	} else {
+		for(auto && s : node.states){
+			if(f(s)) node.mark++;
+		}
 	}
-	if(count >= 2) return true;
+}
+
+splijtboom & lca_impl2(splijtboom & node){
+	if(node.mark > 1) return node;
+	for(auto && c : node.children){
+		if(c.mark > 0) return lca_impl2(c);
+	}
+	return node; // this is a leaf
 }
 
 template <typename Fun>
-const splijtboom & lca(const splijtboom & root, Fun && f){
+splijtboom & lca(splijtboom & root, Fun && f){
 	static_assert(is_same<decltype(f(0)), bool>::value, "f should return a bool");
-	lca_impl(root, f);
+	lca_impl1(root, f);
+	return lca_impl2(root);
 }
 
 int main(int argc, char *argv[]){
@@ -47,22 +67,34 @@ int main(int argc, char *argv[]){
 	const auto Q = g.output_indices.size();
 
 	partition_refine part(N);
+	splijtboom root(N);
 	cout << "starting with " << part.size() << " blocks / " << N << " states" << endl;
 
-	queue<partition_refine::BlockRef> work;
-	const auto push = [&work](auto br){ work.push(br); };
+	queue<pair<partition_refine::BlockRef, reference_wrapper<splijtboom>>> work;
+	const auto push = [&work](auto br, auto & sp){ work.push({br, sp});
+	cout << "pushed "; for(auto && x : sp.states) cout << x; cout << endl; };
 	const auto pop = [&work](){ const auto r = work.front(); work.pop(); return r; };
 
-	push(part.find(0));
+	push(part.find(0), root);
 
 	while(!work.empty()){
-		auto block = pop();
-		if(elems_in(*block) == 1) continue;
+		auto block_boom = pop();
+		auto block = block_boom.first;
+		splijtboom & boom = block_boom.second;
 
-		bool splitted = false;
-		for(int symbol = 0; symbol < P; ++symbol){
+		cout << "current\t";
+		for(auto s : boom.states) cout << s << " ";
+		cout << endl;
+
+		if(boom.states.size() == 1) continue;
+		// if(elems_in(*block) == 1) continue;
+
+		cout << "considering" << endl;
+
+		// First try to split on output
+		for(size_t symbol = 0; symbol < P; ++symbol){
 			auto new_blocks = part.refine(block, [symbol, &g](size_t state){
-				return g.graph[state][symbol].output;
+				return apply(g, state, symbol).output;
 			}, Q);
 
 			if(elems_in(new_blocks) == 1){
@@ -73,14 +105,86 @@ int main(int argc, char *argv[]){
 			}
 
 			// a succesful split, add the children
+			const auto nb = distance(new_blocks.first, new_blocks.second);
+			boom.children.assign(nb, splijtboom(0));
+			boom.seperator = {symbol};
+
+			auto i = 0;
 			while(new_blocks.first != new_blocks.second){
-				push(new_blocks.first++);
+				for(auto && s : *new_blocks.first){
+					boom.children[i].states.push_back(s);
+				}
+
+				push(new_blocks.first++, boom.children[i++]);
 			}
-			splitted = true;
-			break;
+
+			cout << "splitted output into " << nb << endl;
+
+			goto has_split;
 		}
-		if(!splitted) cout << "no split :(" << endl;
+
+		// Then try to split on state
+		for(size_t symbol = 0; symbol < P; ++symbol){
+			vector<bool> successor_states(N, false);
+			for(auto && state : *block){
+				successor_states[g.graph[state][symbol].to] = true;
+			}
+
+			auto & oboom = lca(root, [&successor_states](size_t state) -> bool{
+				return successor_states[state];
+			});
+
+			if(oboom.children.empty()){
+				// a leaf, hence not a split, try other symbols
+				continue;
+			}
+
+			cout << "split\t";
+			for(auto s : oboom.states) cout << s << " ";
+			cout << endl;
+			cout << "into ";
+			for(auto & c : oboom.children) {
+				for(auto s : c.states) cout << s << " ";
+				cout << "- ";
+			}
+			cout << endl;
+
+			// a succesful split, construct the children
+			boom.seperator.resize(oboom.seperator.size() + 1);
+			auto it = begin(boom.seperator);
+			*it++ = symbol;
+			copy(begin(oboom.seperator), end(oboom.seperator), it);
+
+			auto new_blocks = part.refine(block, [&boom, &g](size_t state){
+				return apply(g, state, begin(boom.seperator), end(boom.seperator)).output;
+			}, Q);
+
+			if(elems_in(new_blocks) == 1){
+				throw logic_error("Refinement did not give finer partition, can not happen");
+			}
+
+			const auto nb = distance(new_blocks.first, new_blocks.second);
+			boom.children.assign(nb, splijtboom(0));
+
+			auto i = 0;
+			while(new_blocks.first != new_blocks.second){
+				for(auto && s : *new_blocks.first){
+					boom.children[i].states.push_back(s);
+				}
+
+				push(new_blocks.first++, boom.children[i++]);
+			}
+
+			cout << "splitted state into " << nb << endl;
+
+			goto has_split;
+		}
+		push(block, boom);
+		cout << "no split :(" << endl;
+
+		has_split:
 		cout << "we have " << part.size() << " blocks / " << N << " states" << endl;
+		cout << "and still " << work.size() << " work" << endl << endl;
 	}
 	cout << "jippiejeejjo" << endl;
 }