diff --git a/testsuite/tests/polykinds/T6020a.hs b/testsuite/tests/polykinds/T6020a.hs
new file mode 100644
index 0000000000000000000000000000000000000000..00689786c345dfe0ca199df4dc11d35238b6b226
--- /dev/null
+++ b/testsuite/tests/polykinds/T6020a.hs
@@ -0,0 +1,16 @@
+{-# LANGUAGE DataKinds, FunctionalDependencies, FlexibleInstances,
+              UndecidableInstances, PolyKinds, KindSignatures,
+              ConstraintKinds, FlexibleContexts, GADTs #-}
+
+module T6020a where
+
+class Id (a :: k) (b :: k) | b -> a
+instance a ~ b => Id a b
+
+class Test (x :: a) (y :: a)
+instance (Id x y, Id y z) => Test x z
+
+test :: Test True True => ()
+test = ()
+
+
diff --git a/testsuite/tests/polykinds/T6044.hs b/testsuite/tests/polykinds/T6044.hs
new file mode 100644
index 0000000000000000000000000000000000000000..dd35be90176bc25696fc4206c251b4ec61d31bb8
--- /dev/null
+++ b/testsuite/tests/polykinds/T6044.hs
@@ -0,0 +1,6 @@
+{-# LANGUAGE PolyKinds, DataKinds, TypeFamilies, KindSignatures #-}
+
+module T6044 where
+
+type family Foo (a :: k) :: Maybe k
+type instance Foo a = Just a
diff --git a/testsuite/tests/polykinds/all.T b/testsuite/tests/polykinds/all.T
index 92f6414ac4cafb520ed5d087a110fc5443e6de78..5f136b16b9b21541615e678864c7ceaec9e77cdb 100644
--- a/testsuite/tests/polykinds/all.T
+++ b/testsuite/tests/polykinds/all.T
@@ -41,3 +41,5 @@ test('T6025', normal, run_command, ['$MAKE -s --no-print-directory T6025'])
 test('T6002', normal, compile, [''])
 test('T6039', normal, compile_fail, [''])
 test('T6021', normal, compile_fail, [''])
+test('T6020a', normal, compile, [''])
+test('T6044', normal, compile, [''])