diff --git a/container/autoroot.go b/container/autoroot.go
index 6145ec6..640d72d 100644
--- a/container/autoroot.go
+++ b/container/autoroot.go
@@ -73,7 +73,9 @@ func (r *AutoRootOp) apply(state *setupState) error {
 func (r *AutoRootOp) Is(op Op) bool {
 	vr, ok := op.(*AutoRootOp)
 	return ok && ((r == nil && vr == nil) || (r != nil && vr != nil &&
-		r.Host == vr.Host && r.Prefix == vr.Prefix && r.Flags == vr.Flags))
+		r.Host != nil && vr.Host != nil &&
+		r.Host.String() == vr.Host.String() &&
+		r.Prefix == vr.Prefix && r.Flags == vr.Flags))
 }
 func (*AutoRootOp) prefix() string { return "setting up" }
 func (r *AutoRootOp) String() string {
diff --git a/container/autoroot_test.go b/container/autoroot_test.go
index 7e9d147..77440ac 100644
--- a/container/autoroot_test.go
+++ b/container/autoroot_test.go
@@ -2,6 +2,61 @@ package container
 
 import "testing"
 
+func TestAutoRootOp(t *testing.T) {
+	checkOpsBuilder(t, []opsBuilderTestCase{
+		{"pd", new(Ops).Root(MustAbs("/"), "048090b6ed8f9ebb10e275ff5d8c0659", BindWritable), Ops{
+			&AutoRootOp{
+				Host:   MustAbs("/"),
+				Prefix: "048090b6ed8f9ebb10e275ff5d8c0659",
+				Flags:  BindWritable,
+			},
+		}},
+	})
+
+	checkOpIs(t, []opIsTestCase{
+		{"zero", new(AutoRootOp), new(AutoRootOp), false},
+
+		{"internal ne", &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: ":3",
+			Flags:  BindWritable,
+		}, &AutoRootOp{
+			Host:     MustAbs("/"),
+			Prefix:   ":3",
+			Flags:    BindWritable,
+			resolved: []Op{new(BindMountOp)},
+		}, true},
+
+		{"differs", &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: "\x00",
+			Flags:  BindWritable,
+		}, &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: ":3",
+			Flags:  BindWritable,
+		}, false},
+
+		{"equals", &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: ":3",
+			Flags:  BindWritable,
+		}, &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: ":3",
+			Flags:  BindWritable,
+		}, true},
+	})
+
+	checkOpMeta(t, []opMetaTestCase{
+		{"root", &AutoRootOp{
+			Host:   MustAbs("/"),
+			Prefix: ":3",
+			Flags:  BindWritable,
+		}, "setting up", `auto root "/" prefix :3 flags 0x2`},
+	})
+}
+
 func TestIsAutoRootBindable(t *testing.T) {
 	testCases := []struct {
 		name string
diff --git a/container/mount_test.go b/container/mount_test.go
index eb90477..a400d69 100644
--- a/container/mount_test.go
+++ b/container/mount_test.go
@@ -2,6 +2,7 @@ package container
 
 import (
 	"os"
+	"slices"
 	"testing"
 )
 
@@ -47,3 +48,67 @@ func TestEscapeOverlayDataSegment(t *testing.T) {
 		})
 	}
 }
+
+type opsBuilderTestCase struct {
+	name string
+	ops  *Ops
+	want Ops
+}
+
+func checkOpsBuilder(t *testing.T, testCases []opsBuilderTestCase) {
+	t.Run("build", func(t *testing.T) {
+		for _, tc := range testCases {
+			t.Run(tc.name, func(t *testing.T) {
+				if !slices.EqualFunc(*tc.ops, tc.want, func(op Op, v Op) bool { return op.Is(v) }) {
+					t.Errorf("Ops: %#v, want %#v", tc.ops, tc.want)
+				}
+			})
+		}
+	})
+}
+
+type opIsTestCase struct {
+	name  string
+	op, v Op
+	want  bool
+}
+
+func checkOpIs(t *testing.T, testCases []opIsTestCase) {
+	t.Run("meta", func(t *testing.T) {
+		for _, tc := range testCases {
+			t.Run(tc.name, func(t *testing.T) {
+				if got := tc.op.Is(tc.v); got != tc.want {
+					t.Errorf("Is: %v, want %v", got, tc.want)
+				}
+			})
+		}
+	})
+}
+
+type opMetaTestCase struct {
+	name string
+	op   Op
+
+	wantPrefix string
+	wantString string
+}
+
+func checkOpMeta(t *testing.T, testCases []opMetaTestCase) {
+	t.Run("meta", func(t *testing.T) {
+		for _, tc := range testCases {
+			t.Run(tc.name, func(t *testing.T) {
+				t.Run("prefix", func(t *testing.T) {
+					if got := tc.op.prefix(); got != tc.wantPrefix {
+						t.Errorf("prefix: %q, want %q", got, tc.wantPrefix)
+					}
+				})
+
+				t.Run("string", func(t *testing.T) {
+					if got := tc.op.String(); got != tc.wantString {
+						t.Errorf("String: %s, want %s", got, tc.wantString)
+					}
+				})
+			})
+		}
+	})
+}