diff --git a/tests/e2e/test_system_sae.py b/tests/e2e/test_system_sae.py
index b520c34..080b58b 100644
--- a/tests/e2e/test_system_sae.py
+++ b/tests/e2e/test_system_sae.py
@@ -134,3 +134,30 @@ class TestSAECompression:
         compressed = sae._compress_xml(broken_xml)
         assert "PACKAGES: com.instagram.android" in compressed
         assert "TEXTS: Hello" in compressed
+
+
+class TestSAELoop:
+    """Tests the higher-level engine loops."""
+
+    def test_ensure_clear_screen_returns_true_immediately_if_normal(self, sae):
+        """If the screen is NORMAL, the SAE should return True without taking actions."""
+        xml_dump = '''
+        <node package="com.instagram.android">
+            <node resource-id="com.instagram.android:id/row_feed_button_like" />
+        </node>
+        '''
+        # Bypass dump_hierarchy
+        sae.device.dump_hierarchy = lambda: xml_dump
+        assert sae.ensure_clear_screen(max_attempts=3) is True
+        assert sae._consecutive_failures == 0
+
+    def test_is_instagram_foreground(self, sae):
+        xml_dump = '''
+        <node package="com.instagram.android">
+            <node resource-id="com.instagram.android:id/row_feed_button_like" />
+        </node>
+        '''
+        assert sae.is_instagram_foreground(xml_dump=xml_dump) is True
+
+        foreign_xml = '<node package="com.apple.ios" />'
+        assert sae.is_instagram_foreground(xml_dump=foreign_xml) is False