diff --git a/loopy/kernel/__init__.py b/loopy/kernel/__init__.py
index da15967c6a0e6ec4826bc229e85e28216c5f2ee9..174b6c43ab7ca43df104e9ec5f232003bdd71e7a 100644
--- a/loopy/kernel/__init__.py
+++ b/loopy/kernel/__init__.py
@@ -76,6 +76,9 @@ class _UniqueVarNameGenerator(UniqueNameGenerator):
         # names by appending '_s<NUMBER>'. Make sure that no
         # conflicts can arise from these names.
 
+        # Case 1: a_s0 is already a name, we are trying to insert a
+        # Case 2: a is already a name, we are trying to insert a_s0
+
         if name in self.array_prefixes:
             return True