diff --git a/main.go b/main.go
index a2920d8..ea12361 100644
--- a/main.go
+++ b/main.go
@@ -129,32 +129,16 @@ func thompson(re string) *State {
 		case CONCAT:
 			s2 := mustPop(&nfa)
 			s1 := mustPop(&nfa)
-			for i := range s1.output {
-				s1.output[i].transitions[s2.content] = append(s1.output[i].transitions[s2.content], s2)
-			}
-			s1.output = s2.output
+			s1 = concatenate(s1, s2)
 			nfa = append(nfa, s1)
 		case '*': // Create a 0-state, concat the popped state after it, concat the 0-state after the popped state
 			s1 := mustPop(&nfa)
-			stateToAdd := &State{}
-			stateToAdd.transitions = make(map[int][]*State)
-			stateToAdd.content = EPSILON
-			stateToAdd.isEmpty = true
-			stateToAdd.isKleene = true
-			stateToAdd.output = append(stateToAdd.output, stateToAdd)
-			for i := range s1.output {
-				s1.output[i].transitions[stateToAdd.content] = append(s1.output[i].transitions[stateToAdd.content], stateToAdd)
-			}
-			stateToAdd.transitions[s1.content] = append(stateToAdd.transitions[s1.content], s1)
+			stateToAdd := kleene(*s1)
 			nfa = append(nfa, stateToAdd)
-		case '+':
+		case '+': // a+ is equivalent to aa*
 			s1 := mustPop(&nfa)
-			for i := range s1.output {
-				s1.output[i].transitions[s1.content] = append(s1.output[i].transitions[s1.content], s1)
-			}
-			// Reset output to s1 (in case s1 was a union operator state, which has multiple outputs)
-			s1.output = nil
-			s1.output = append(s1.output, s1)
+			s2 := kleene(*s1)
+			s1 = concatenate(s1, s2)
 			nfa = append(nfa, s1)
 		case '|':
 			s1 := mustPop(&nfa)