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diff --git a/t/t6600-test-reach.sh b/t/t6600-test-reach.sh
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+#!/bin/sh
+
+test_description='basic commit reachability tests'
+
+. ./test-lib.sh
+
+# Construct a grid-like commit graph with points (x,y)
+# with 1 <= x <= 10, 1 <= y <= 10, where (x,y) has
+# parents (x-1, y) and (x, y-1), keeping in mind that
+# we drop a parent if a coordinate is nonpositive.
+#
+#             (10,10)
+#            /       \
+#         (10,9)    (9,10)
+#        /     \   /      \
+#    (10,8)    (9,9)      (8,10)
+#   /     \    /   \      /    \
+#         ( continued...)
+#   \     /    \   /      \    /
+#    (3,1)     (2,2)      (1,3)
+#        \     /    \     /
+#         (2,1)      (2,1)
+#              \    /
+#              (1,1)
+#
+# We use branch 'commit-x-y' to refer to (x,y).
+# This grid allows interesting reachability and
+# non-reachability queries: (x,y) can reach (x',y')
+# if and only if x' <= x and y' <= y.
+test_expect_success 'setup' '
+	for i in $(test_seq 1 10)
+	do
+		test_commit "1-$i" &&
+		git branch -f commit-1-$i
+	done &&
+	for j in $(test_seq 1 9)
+	do
+		git reset --hard commit-$j-1 &&
+		x=$(($j + 1)) &&
+		test_commit "$x-1" &&
+		git branch -f commit-$x-1 &&
+
+		for i in $(test_seq 2 10)
+		do
+			git merge commit-$j-$i -m "$x-$i" &&
+			git branch -f commit-$x-$i
+		done
+	done &&
+	git commit-graph write --reachable &&
+	mv .git/objects/info/commit-graph commit-graph-full &&
+	git show-ref -s commit-5-5 | git commit-graph write --stdin-commits &&
+	mv .git/objects/info/commit-graph commit-graph-half &&
+	git config core.commitGraph true
+'
+
+test_three_modes () {
+	test_when_finished rm -rf .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual &&
+	cp commit-graph-full .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual &&
+	cp commit-graph-half .git/objects/info/commit-graph &&
+	test-tool reach $1 <input >actual &&
+	test_cmp expect actual
+}
+
+test_expect_success 'ref_newer:miss' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	B:commit-4-9
+	EOF
+	echo "ref_newer(A,B):0" >expect &&
+	test_three_modes ref_newer
+'
+
+test_expect_success 'ref_newer:hit' '
+	cat >input <<-\EOF &&
+	A:commit-5-7
+	B:commit-2-3
+	EOF
+	echo "ref_newer(A,B):1" >expect &&
+	test_three_modes ref_newer
+'
+
+test_done