diff --git a/frontend/src/mathjax-proof-tree.ts b/frontend/src/mathjax-proof-tree.ts
index 8ea64d1..5365670 100644
--- a/frontend/src/mathjax-proof-tree.ts
+++ b/frontend/src/mathjax-proof-tree.ts
@@ -26,9 +26,10 @@ class MathjaxProofTree extends MathjaxAdapter {
 
     protected calculateSteps(): void {
         if (this.shadowRoot !== null) {
+            const root = this.shadowRoot;
             let semanticsMatch = (semantics: string) => semantics.indexOf("bspr_inference:") >= 0;
             // first, enumerate all of the steps
-            let nodeIterator = document.createNodeIterator(this.shadowRoot, NodeFilter.SHOW_ELEMENT);
+            let nodeIterator = document.createNodeIterator(root, NodeFilter.SHOW_ELEMENT);
             let steps = [];
             let a = null;
             let stepIdx = 0;
@@ -44,7 +45,7 @@ class MathjaxProofTree extends MathjaxAdapter {
                 }
             }
             // then fix some more mathjax layout issues
-            for (const step of this.shadowRoot.querySelectorAll<HTMLElement>('g[typicalc="step"]')) {
+            for (const step of root.querySelectorAll<HTMLElement>('g[typicalc="step"]')) {
                 const infRule = step.querySelector<HTMLElement>('g[semantics="bspr_inferenceRule:down"]');
                 if (infRule === null) {
                     continue;
@@ -78,7 +79,7 @@ class MathjaxProofTree extends MathjaxAdapter {
                 stepAbove.transform.baseVal[0].matrix.e -= dx;
             }
             // then create the steps
-            nodeIterator = document.createNodeIterator(this.shadowRoot, NodeFilter.SHOW_ELEMENT);
+            nodeIterator = document.createNodeIterator(root, NodeFilter.SHOW_ELEMENT);
             steps = [];
             stepIdx = 0;
             while (a = nodeIterator.nextNode() as HTMLElement) {
@@ -122,7 +123,7 @@ class MathjaxProofTree extends MathjaxAdapter {
                     steps.push([a, above]);
                 }
             }
-            const svg = this.shadowRoot.querySelector<SVGElement>("svg")!;
+            const svg = root.querySelector<SVGElement>("svg")!;
             const nodeIterator2 = [...svg.querySelectorAll<SVGGraphicsElement>("g[data-mml-node='mtr']")];
             // start layout fixes in the innermost part of the SVG
             nodeIterator2.reverse();
@@ -170,9 +171,9 @@ class MathjaxProofTree extends MathjaxAdapter {
                     i += 1;
                 }
             }
-            const bbox = (svg.childNodes[1] as SVGGraphicsElement).getBBox();
-            // TODO: this does not work when using a permalink
-            svg.setAttribute("viewBox", bbox.x + " " + bbox.y + " " + bbox.width + " " + bbox.height);
+            // TODO: this does not scale the SVG correctly
+            //const bbox = (svg.childNodes[1] as SVGGraphicsElement).getBBox();
+            //svg.setAttribute("viewBox", bbox.x + " " + bbox.y + " " + bbox.width + " " + bbox.height);
             if (counter >= 3) {
                 // should not be used on empty SVGs
                 // @ts-ignore
diff --git a/frontend/styles/view/main/input-bar.css b/frontend/styles/view/main/input-bar.css
index 0c164b3..37a9b0c 100644
--- a/frontend/styles/view/main/input-bar.css
+++ b/frontend/styles/view/main/input-bar.css
@@ -1,13 +1,5 @@
-@media (max-width: 500px) {
-    #inputField {
-		width: 20em;
-	}
-}
-
-@media (min-width: 1000px) {
-    #inputField {
-		width: 30em;
-	}
+#inputField {
+	flex-grow: 1;
 }
 
 #inputField {
@@ -16,6 +8,7 @@
 
 #inputBar {
 	align-items: center;
+	padding: 1em;
 }
 
 vaadin-drawer-toggle {
diff --git a/frontend/styles/view/main/upper-bar.css b/frontend/styles/view/main/upper-bar.css
index cbc2493..d311ca2 100644
--- a/frontend/styles/view/main/upper-bar.css
+++ b/frontend/styles/view/main/upper-bar.css
@@ -19,31 +19,13 @@
 }
 
 #helpIcon {
-	margin-left: auto;
+	margin-left: 1em;
 	margin-right: 1em;
 }
 
-@media (max-width: 500px) {
-   	#inputBar {
-		margin: auto;
-	}
-
-	#viewTitle {
-		margin-right: 5em;
-	}
-}
-
-@media (min-width: 1000px) {
-    #inputBar {
-		margin-left: 15em;
-	}
-
-	#viewTitle {
-		margin-right: auto;
-	}
+#inputBar {
+	flex-grow: 1;
+	justify-content: end;
 }
 
 
-
-
-
diff --git a/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java b/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
index 560e5fc..d565f40 100644
--- a/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
+++ b/src/main/java/edu/kit/typicalc/model/TypeInferenceResult.java
@@ -63,9 +63,6 @@ public class TypeInferenceResult {
             }
         }
         return typeVar;
-        // TODO: correct?
-//        throw new IllegalStateException("MGU has to contain substitution for original type variable: "
-//                + typeVar.toString());
     }
 
     /**
diff --git a/src/main/java/edu/kit/typicalc/view/main/ExampleDialog.java b/src/main/java/edu/kit/typicalc/view/main/ExampleDialog.java
index 1dd36be..594fe57 100644
--- a/src/main/java/edu/kit/typicalc/view/main/ExampleDialog.java
+++ b/src/main/java/edu/kit/typicalc/view/main/ExampleDialog.java
@@ -23,7 +23,7 @@ public class ExampleDialog extends Dialog implements LocaleChangeObserver {
 
     private static final List<String> EXAMPLES =
             List.of("λx.x", "λx.λy.y x", "λx.λy.y (x x)", "let f = λx. g y y in f 3", "(λx.x x) (λx.x x)",
-                    "(λx.λy.y (x x)) (λz. λa. z g a)");
+                    "(λx.λy.y (x y)) (λz. λa. z g a)");
     private final Paragraph instruction;
 
     /**
diff --git a/src/main/java/edu/kit/typicalc/view/main/InputBar.java b/src/main/java/edu/kit/typicalc/view/main/InputBar.java
index c7757dd..f348a0f 100644
--- a/src/main/java/edu/kit/typicalc/view/main/InputBar.java
+++ b/src/main/java/edu/kit/typicalc/view/main/InputBar.java
@@ -1,6 +1,7 @@
 package edu.kit.typicalc.view.main;
 
 import com.vaadin.flow.component.Key;
+import com.vaadin.flow.component.UI;
 import com.vaadin.flow.component.button.Button;
 import com.vaadin.flow.component.button.ButtonVariant;
 import com.vaadin.flow.component.dependency.CssImport;
@@ -81,7 +82,10 @@ public class InputBar extends HorizontalLayout implements LocaleChangeObserver {
      */
     protected void inferTerm(String term) {
         inputField.setValue(term);
-        inferTypeButton.click();
+        // for some reason the Vaadin "click" does not work
+        //inferTypeButton.click();
+        UI.getCurrent().getPage().executeJs(
+                String.format("document.getElementById('%s').click()", INFER_BUTTON_ID));
     }
 
     private void onInputFieldValueChange() {
@@ -93,6 +97,7 @@ public class InputBar extends HorizontalLayout implements LocaleChangeObserver {
         String currentInput = inputField.getOptionalValue().orElse(StringUtils.EMPTY);
 
         if (currentInput.length() < MAX_INPUT_LENGTH) {
+            UI.getCurrent().getPage().setTitle(getTranslation("root.typicalc") + " - " + currentInput);
             callback.accept(Pair.of(currentInput, typeAssumptionsArea.getTypeAssumptions()));
         } else {
             final Notification errorNotification = new ErrorNotification(getTranslation("root.overlongInput"));