diff --git a/src/nfa.rs b/src/nfa.rs
index b46ecb9..a2ea489 100644
--- a/src/nfa.rs
+++ b/src/nfa.rs
@@ -44,22 +44,19 @@ pub enum StateOrdering {
 impl Nfa {
     /// checks if the nfa is complete:
     /// every state has an outgoing transition for every letter in the alphabet
-    ///
-    /// TODO: this uses equality on (sorted) vectors. Are HashSets better?
     pub fn is_complete(&self) -> bool {
         // get the alphabet
         let mut letters = self.get_alphabet();
         letters.sort();
         // for each state, check if it has a transition for each letter in the alphabet
         for state in 0..self.nb_states() {
-            let mut state_actions = self
+            let state_actions = self
                 .transitions
                 .iter()
                 .filter(|t| t.from == state)
                 .map(|t| t.label.clone())
-                .collect::<Vec<_>>();
-            state_actions.sort();
-            if state_actions != letters {
+                .collect::<std::collections::BTreeSet<_>>();
+            if !letters.iter().all(|l| state_actions.contains(*l)) {
                 return false;
             }
         }
@@ -563,6 +560,18 @@ mod test {
         assert!(nfa.is_complete());
     }
     #[test]
+    fn is_complete3() {
+        let mut nfa = Nfa::from_size(2);
+        nfa.add_transition_by_index1(0, 1, 'a');
+        nfa.add_transition_by_index1(0, 1, 'b');
+        nfa.add_transition_by_index1(1, 0, 'a');
+        nfa.add_transition_by_index1(1, 0, 'b');
+
+        // in addition, we add a second a-edge from state 0.
+        nfa.add_transition_by_index1(0, 0, 'a');
+        assert!(nfa.is_complete());
+    }
+    #[test]
     fn complete_to_selfloops() {
         // this NFA is missing a 'b'-strep from state 1.
         // after completion, there should be a step 1 -b-> 1.