diff --git a/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java b/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
index 8337057..0dd73bc 100644
--- a/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
+++ b/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
@@ -4,6 +4,7 @@ import edu.kit.typicalc.model.type.Type;
 import edu.kit.typicalc.model.type.TypeVariable;
 
 import java.util.ArrayList;
+import java.util.Comparator;
 import java.util.List;
 
 /**
@@ -28,6 +29,8 @@ public class TypeInferenceResult {
     protected TypeInferenceResult(List<Substitution> substitutions, TypeVariable typeVar) {
         MGU = new ArrayList<>(substitutions);
         findMGU();
+        MGU.sort(Comparator.comparingInt((Substitution o) ->
+                o.getVariable().getIndex()).thenComparing(o -> o.getVariable().getKind()));
         finalType = findFinalType(typeVar);
     }
 
diff --git a/src/main/java/edu/kit/typicalc/model/type/FunctionType.java b/src/main/java/edu/kit/typicalc/model/type/FunctionType.java
index b905c6c..1d84a00 100644
--- a/src/main/java/edu/kit/typicalc/model/type/FunctionType.java
+++ b/src/main/java/edu/kit/typicalc/model/type/FunctionType.java
@@ -114,6 +114,11 @@ public class FunctionType extends Type {
         return parameter;
     }
 
+    @Override
+    public String toString() {
+        return "FunctionType[" + parameter + " -> " + output + ']';
+    }
+
     @Override
     public boolean equals(Object o) {
         if (this == o) {
diff --git a/src/main/java/edu/kit/typicalc/model/type/TypeVariableKind.java b/src/main/java/edu/kit/typicalc/model/type/TypeVariableKind.java
index f7824cc..53dd92b 100644
--- a/src/main/java/edu/kit/typicalc/model/type/TypeVariableKind.java
+++ b/src/main/java/edu/kit/typicalc/model/type/TypeVariableKind.java
@@ -5,16 +5,16 @@ package edu.kit.typicalc.model.type;
  */
 public enum TypeVariableKind {
 
-    /**
-     * Used if the type variable was created from user input.
-     */
-    USER_INPUT,
-
     /**
      * Used if the type variable was generated while building the proof tree.
      */
     TREE,
 
+    /**
+     * Used if the type variable was created from user input.
+     */
+    USER_INPUT,
+
     /**
      * Used if the type variable was generated for a type assumption of a free variable in the input lambda term.
      */
diff --git a/src/test/java/edu/kit/typicalc/model/TypeInferenceResultTest.java b/src/test/java/edu/kit/typicalc/model/TypeInferenceResultTest.java
index a4cdbfd..df6953c 100644
--- a/src/test/java/edu/kit/typicalc/model/TypeInferenceResultTest.java
+++ b/src/test/java/edu/kit/typicalc/model/TypeInferenceResultTest.java
@@ -1,4 +1,58 @@
 package edu.kit.typicalc.model;
 
+import edu.kit.typicalc.model.type.FunctionType;
+import edu.kit.typicalc.model.type.TypeVariable;
+import edu.kit.typicalc.model.type.TypeVariableKind;
+import org.junit.jupiter.api.Test;
+
+import java.util.ArrayList;
+import java.util.Arrays;
+import java.util.List;
+
+import static org.junit.jupiter.api.Assertions.assertEquals;
+
 class TypeInferenceResultTest {
+
+    private static final TypeVariable A_1 = new TypeVariable(TypeVariableKind.TREE, 1);
+    private static final TypeVariable A_2 = new TypeVariable(TypeVariableKind.TREE, 2);
+    private static final TypeVariable A_3 = new TypeVariable(TypeVariableKind.TREE, 3);
+    private static final TypeVariable A_4 = new TypeVariable(TypeVariableKind.TREE, 4);
+    private static final TypeVariable A_5 = new TypeVariable(TypeVariableKind.TREE, 5);
+    private static final TypeVariable A_6 = new TypeVariable(TypeVariableKind.TREE, 6);
+    private static final TypeVariable A_7 = new TypeVariable(TypeVariableKind.TREE, 7);
+
+    @Test
+    void getMGU() {
+        // rectified example from introduction slides
+        List<Substitution> substitutions = new ArrayList<>(Arrays.asList(
+                new Substitution(A_7, A_2),
+                new Substitution(A_4, new FunctionType(A_7, A_5)),
+                new Substitution(A_6, new FunctionType(A_7, A_5)),
+                new Substitution(A_3, new FunctionType(A_4, A_5)),
+                new Substitution(A_1, new FunctionType(A_2, A_3))
+        ));
+        TypeInferenceResult result = new TypeInferenceResult(substitutions, A_1);
+
+        List<Substitution> expectedMGU = new ArrayList<>(Arrays.asList(
+                new Substitution(A_1, new FunctionType(A_2, new FunctionType(new FunctionType(A_2, A_5), A_5))),
+                new Substitution(A_3, new FunctionType(new FunctionType(A_2, A_5), A_5)),
+                new Substitution(A_4, new FunctionType(A_2, A_5)),
+                new Substitution(A_6, new FunctionType(A_2, A_5)),
+                new Substitution(A_7, A_2)
+        ));
+
+        assertEquals(expectedMGU, result.getMGU());
+
+        // tests if mgu-generation works for substitutions given in reverse order
+        List<Substitution> substitutions2 = new ArrayList<>(Arrays.asList(
+                new Substitution(A_1, new FunctionType(A_2, A_3)),
+                new Substitution(A_3, new FunctionType(A_4, A_5)),
+                new Substitution(A_6, new FunctionType(A_7, A_5)),
+                new Substitution(A_4, new FunctionType(A_7, A_5)),
+                new Substitution(A_7, A_2)
+        ));
+        TypeInferenceResult result2 = new TypeInferenceResult(substitutions2, A_1);
+
+        assertEquals(expectedMGU, result2.getMGU());
+    }
 }