diff --git a/mlir/include/mlir/IR/Dominance.h b/mlir/include/mlir/IR/Dominance.h
index 2536ce585b3fd..95c99bd59f7b2 100644
--- a/mlir/include/mlir/IR/Dominance.h
+++ b/mlir/include/mlir/IR/Dominance.h
@@ -141,8 +141,8 @@ class DominanceInfo : public detail::DominanceInfoBase</*IsPostDom=*/false> {
   /// are in the same block and A properly dominates B within the block, or if
   /// the block that contains A properly dominates the block that contains B. In
   /// an SSACFG region, Operation A dominates Operation B in the same block if A
-  /// preceeds B. In a Graph region, all operations in a block dominate all
-  /// other operations in the same block.
+  /// preceeds B. In a Graph region, all operations in a block properly dominate
+  /// all operations in the same block.
   ///
   /// The `enclosingOpOk` flag says whether we should return true if the B op
   /// is enclosed by a region on A.
@@ -176,9 +176,14 @@ class DominanceInfo : public detail::DominanceInfoBase</*IsPostDom=*/false> {
   /// Return true if the specified block A properly dominates block B, i.e.: if
   /// block A contains block B, or if the region which contains block A also
   /// contains block B or some parent of block B and block A dominates that
-  /// block in that kind of region. In an SSACFG region, block A dominates
-  /// block B if all control flow paths from the entry block to block B flow
-  /// through block A. In a Graph region, all blocks dominate all other blocks.
+  /// block in that kind of region.
+  ///
+  /// In an SSACFG region, block A dominates block B if all control flow paths
+  /// from the entry block to block B flow through block A.
+  ///
+  /// Graph regions have only a single block. To be consistent with "proper
+  /// dominance" of ops, the single block is considered to properly dominate
+  /// itself in a graph region.
   bool properlyDominates(Block *a, Block *b) const {
     return super::properlyDominates(a, b);
   }
diff --git a/mlir/lib/IR/Dominance.cpp b/mlir/lib/IR/Dominance.cpp
index 2b138ae223546..31f7e7dbc925c 100644
--- a/mlir/lib/IR/Dominance.cpp
+++ b/mlir/lib/IR/Dominance.cpp
@@ -34,7 +34,8 @@ DominanceInfoBase<IsPostDom>::~DominanceInfoBase() {
     delete entry.second.getPointer();
 }
 
-template <bool IsPostDom> void DominanceInfoBase<IsPostDom>::invalidate() {
+template <bool IsPostDom>
+void DominanceInfoBase<IsPostDom>::invalidate() {
   for (auto entry : dominanceInfos)
     delete entry.second.getPointer();
   dominanceInfos.clear();
@@ -217,9 +218,10 @@ template <bool IsPostDom>
 bool DominanceInfoBase<IsPostDom>::properlyDominates(Block *a, Block *b) const {
   assert(a && b && "null blocks not allowed");
 
-  // A block dominates itself but does not properly dominate itself.
+  // A block dominates, but does not properly dominate, itself unless this
+  // is a graph region.
   if (a == b)
-    return false;
+    return !hasSSADominance(a);
 
   // If both blocks are not in the same region, `a` properly dominates `b` if
   // `b` is defined in an operation region that (recursively) ends up being
@@ -269,7 +271,7 @@ bool DominanceInfo::properlyDominatesImpl(Operation *a, Operation *b,
   Block *aBlock = a->getBlock(), *bBlock = b->getBlock();
   assert(aBlock && bBlock && "operations must be in a block");
 
-  // An instruction dominates, but does not properlyDominate, itself unless this
+  // An operation dominates, but does not properly dominate, itself unless this
   // is a graph region.
   if (a == b)
     return !hasSSADominance(aBlock);
diff --git a/mlir/test/Analysis/test-dominance.mlir b/mlir/test/Analysis/test-dominance.mlir
index 3c53193db7f72..a926a8271200a 100644
--- a/mlir/test/Analysis/test-dominance.mlir
+++ b/mlir/test/Analysis/test-dominance.mlir
@@ -1,4 +1,4 @@
-// RUN: mlir-opt %s -pass-pipeline="builtin.module(func.func(test-print-dominance))" -split-input-file 2>&1 | FileCheck %s
+// RUN: mlir-opt %s -pass-pipeline="builtin.module(func.func(test-print-dominance))" -split-input-file | FileCheck %s
 
 // CHECK-LABEL: Testing : func_condBranch
 func.func @func_condBranch(%cond : i1) {
@@ -10,40 +10,117 @@ func.func @func_condBranch(%cond : i1) {
 ^exit:
   return
 }
-// CHECK-LABEL: --- DominanceInfo ---
-// CHECK-NEXT: Nearest(0, 0) = 0
-// CHECK-NEXT: Nearest(0, 1) = 0
-// CHECK-NEXT: Nearest(0, 2) = 0
-// CHECK-NEXT: Nearest(0, 3) = 0
+
+// CHECK: --- DominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 0
+// CHECK: Nearest(0, 2) = 0
+// CHECK: Nearest(0, 3) = 0
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 0
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 0
-// CHECK-NEXT: Nearest(1, 3) = 0
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 0
+// CHECK: Nearest(1, 3) = 0
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 0
-// CHECK-NEXT: Nearest(2, 1) = 0
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 0
+// CHECK: Nearest(2, 1) = 0
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 0
+// CHECK: Nearest(2, 4) = 4
 // CHECK: Nearest(3, 0) = 0
-// CHECK-NEXT: Nearest(3, 1) = 0
-// CHECK-NEXT: Nearest(3, 2) = 0
-// CHECK-NEXT: Nearest(3, 3) = 3
-// CHECK-LABEL: --- PostDominanceInfo ---
-// CHECK-NEXT: Nearest(0, 0) = 0
-// CHECK-NEXT: Nearest(0, 1) = 3
-// CHECK-NEXT: Nearest(0, 2) = 3
-// CHECK-NEXT: Nearest(0, 3) = 3
+// CHECK: Nearest(3, 1) = 0
+// CHECK: Nearest(3, 2) = 0
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- PostDominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 3
+// CHECK: Nearest(0, 2) = 3
+// CHECK: Nearest(0, 3) = 3
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 3
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 3
-// CHECK-NEXT: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 3
+// CHECK: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 3
-// CHECK-NEXT: Nearest(2, 1) = 3
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 1) = 3
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 4) = 4
 // CHECK: Nearest(3, 0) = 3
-// CHECK-NEXT: Nearest(3, 1) = 3
-// CHECK-NEXT: Nearest(3, 2) = 3
-// CHECK-NEXT: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 1) = 3
+// CHECK: Nearest(3, 2) = 3
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- Block Dominance relationship ---
+// CHECK: dominates(0, 0) = 1 (properly = 0)
+// CHECK: dominates(0, 1) = 1 (properly = 1)
+// CHECK: dominates(0, 2) = 1 (properly = 1)
+// CHECK: dominates(0, 3) = 1 (properly = 1)
+// CHECK: dominates(0, 4) = 0 (properly = 0)
+// CHECK: dominates(1, 0) = 0 (properly = 0)
+// CHECK: dominates(1, 1) = 1 (properly = 0)
+// CHECK: dominates(1, 2) = 0 (properly = 0)
+// CHECK: dominates(1, 3) = 0 (properly = 0)
+// CHECK: dominates(1, 4) = 0 (properly = 0)
+// CHECK: dominates(2, 0) = 0 (properly = 0)
+// CHECK: dominates(2, 1) = 0 (properly = 0)
+// CHECK: dominates(2, 2) = 1 (properly = 0)
+// CHECK: dominates(2, 3) = 0 (properly = 0)
+// CHECK: dominates(2, 4) = 0 (properly = 0)
+// CHECK: dominates(3, 0) = 0 (properly = 0)
+// CHECK: dominates(3, 1) = 0 (properly = 0)
+// CHECK: dominates(3, 2) = 0 (properly = 0)
+// CHECK: dominates(3, 3) = 1 (properly = 0)
+// CHECK: dominates(3, 4) = 0 (properly = 0)
+// CHECK: dominates(4, 0) = 1 (properly = 1)
+// CHECK: dominates(4, 1) = 1 (properly = 1)
+// CHECK: dominates(4, 2) = 1 (properly = 1)
+// CHECK: dominates(4, 3) = 1 (properly = 1)
+// CHECK: dominates(4, 4) = 1 (properly = 1)
+
+// CHECK: --- Block PostDominance relationship ---
+// CHECK: postdominates(0, 0) = 1 (properly = 0)
+// CHECK: postdominates(0, 1) = 0 (properly = 0)
+// CHECK: postdominates(0, 2) = 0 (properly = 0)
+// CHECK: postdominates(0, 3) = 0 (properly = 0)
+// CHECK: postdominates(0, 4) = 0 (properly = 0)
+// CHECK: postdominates(1, 0) = 0 (properly = 0)
+// CHECK: postdominates(1, 1) = 1 (properly = 0)
+// CHECK: postdominates(1, 2) = 0 (properly = 0)
+// CHECK: postdominates(1, 3) = 0 (properly = 0)
+// CHECK: postdominates(1, 4) = 0 (properly = 0)
+// CHECK: postdominates(2, 0) = 0 (properly = 0)
+// CHECK: postdominates(2, 1) = 0 (properly = 0)
+// CHECK: postdominates(2, 2) = 1 (properly = 0)
+// CHECK: postdominates(2, 3) = 0 (properly = 0)
+// CHECK: postdominates(2, 4) = 0 (properly = 0)
+// CHECK: postdominates(3, 0) = 1 (properly = 1)
+// CHECK: postdominates(3, 1) = 1 (properly = 1)
+// CHECK: postdominates(3, 2) = 1 (properly = 1)
+// CHECK: postdominates(3, 3) = 1 (properly = 0)
+// CHECK: postdominates(3, 4) = 0 (properly = 0)
+// CHECK: postdominates(4, 0) = 1 (properly = 1)
+// CHECK: postdominates(4, 1) = 1 (properly = 1)
+// CHECK: postdominates(4, 2) = 1 (properly = 1)
+// CHECK: postdominates(4, 3) = 1 (properly = 1)
+// CHECK: postdominates(4, 4) = 1 (properly = 1)
+
+// CHECK: module attributes {test.block_ids = array<i64: 4>}
+// CHECK:   func.func @func_condBranch({{.*}}) attributes {test.block_ids = array<i64: 0, 1, 2, 3>}
 
 // -----
 
@@ -60,32 +137,117 @@ func.func @func_loop(%arg0 : i32, %arg1 : i32) {
 ^exit:
   return
 }
-// CHECK-LABEL: --- DominanceInfo ---
+
+// CHECK: --- DominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 0
+// CHECK: Nearest(0, 2) = 0
+// CHECK: Nearest(0, 3) = 0
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 0
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 1
-// CHECK-NEXT: Nearest(1, 3) = 1
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 1
+// CHECK: Nearest(1, 3) = 1
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 0
-// CHECK-NEXT: Nearest(2, 1) = 1
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 1
+// CHECK: Nearest(2, 1) = 1
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 1
+// CHECK: Nearest(2, 4) = 4
 // CHECK: Nearest(3, 0) = 0
-// CHECK-NEXT: Nearest(3, 1) = 1
-// CHECK-NEXT: Nearest(3, 2) = 1
-// CHECK-NEXT: Nearest(3, 3) = 3
-// CHECK-LABEL: --- PostDominanceInfo ---
+// CHECK: Nearest(3, 1) = 1
+// CHECK: Nearest(3, 2) = 1
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- PostDominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 1
+// CHECK: Nearest(0, 3) = 3
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 1
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 1
-// CHECK-NEXT: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 1
+// CHECK: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 1
-// CHECK-NEXT: Nearest(2, 1) = 1
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 1) = 1
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 4) = 4
 // CHECK: Nearest(3, 0) = 3
-// CHECK-NEXT: Nearest(3, 1) = 3
-// CHECK-NEXT: Nearest(3, 2) = 3
-// CHECK-NEXT: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 1) = 3
+// CHECK: Nearest(3, 2) = 3
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- Block Dominance relationship ---
+// CHECK: dominates(0, 0) = 1 (properly = 0)
+// CHECK: dominates(0, 1) = 1 (properly = 1)
+// CHECK: dominates(0, 2) = 1 (properly = 1)
+// CHECK: dominates(0, 3) = 1 (properly = 1)
+// CHECK: dominates(0, 4) = 0 (properly = 0)
+// CHECK: dominates(1, 0) = 0 (properly = 0)
+// CHECK: dominates(1, 1) = 1 (properly = 0)
+// CHECK: dominates(1, 2) = 1 (properly = 1)
+// CHECK: dominates(1, 3) = 1 (properly = 1)
+// CHECK: dominates(1, 4) = 0 (properly = 0)
+// CHECK: dominates(2, 0) = 0 (properly = 0)
+// CHECK: dominates(2, 1) = 0 (properly = 0)
+// CHECK: dominates(2, 2) = 1 (properly = 0)
+// CHECK: dominates(2, 3) = 0 (properly = 0)
+// CHECK: dominates(2, 4) = 0 (properly = 0)
+// CHECK: dominates(3, 0) = 0 (properly = 0)
+// CHECK: dominates(3, 1) = 0 (properly = 0)
+// CHECK: dominates(3, 2) = 0 (properly = 0)
+// CHECK: dominates(3, 3) = 1 (properly = 0)
+// CHECK: dominates(3, 4) = 0 (properly = 0)
+// CHECK: dominates(4, 0) = 1 (properly = 1)
+// CHECK: dominates(4, 1) = 1 (properly = 1)
+// CHECK: dominates(4, 2) = 1 (properly = 1)
+// CHECK: dominates(4, 3) = 1 (properly = 1)
+// CHECK: dominates(4, 4) = 1 (properly = 1)
+
+// CHECK: --- Block PostDominance relationship ---
+// CHECK: postdominates(0, 0) = 1 (properly = 0)
+// CHECK: postdominates(0, 1) = 0 (properly = 0)
+// CHECK: postdominates(0, 2) = 0 (properly = 0)
+// CHECK: postdominates(0, 3) = 0 (properly = 0)
+// CHECK: postdominates(0, 4) = 0 (properly = 0)
+// CHECK: postdominates(1, 0) = 1 (properly = 1)
+// CHECK: postdominates(1, 1) = 1 (properly = 0)
+// CHECK: postdominates(1, 2) = 1 (properly = 1)
+// CHECK: postdominates(1, 3) = 0 (properly = 0)
+// CHECK: postdominates(1, 4) = 0 (properly = 0)
+// CHECK: postdominates(2, 0) = 0 (properly = 0)
+// CHECK: postdominates(2, 1) = 0 (properly = 0)
+// CHECK: postdominates(2, 2) = 1 (properly = 0)
+// CHECK: postdominates(2, 3) = 0 (properly = 0)
+// CHECK: postdominates(2, 4) = 0 (properly = 0)
+// CHECK: postdominates(3, 0) = 1 (properly = 1)
+// CHECK: postdominates(3, 1) = 1 (properly = 1)
+// CHECK: postdominates(3, 2) = 1 (properly = 1)
+// CHECK: postdominates(3, 3) = 1 (properly = 0)
+// CHECK: postdominates(3, 4) = 0 (properly = 0)
+// CHECK: postdominates(4, 0) = 1 (properly = 1)
+// CHECK: postdominates(4, 1) = 1 (properly = 1)
+// CHECK: postdominates(4, 2) = 1 (properly = 1)
+// CHECK: postdominates(4, 3) = 1 (properly = 1)
+// CHECK: postdominates(4, 4) = 1 (properly = 1)
+
+// CHECK: module attributes {test.block_ids = array<i64: 4>}
+// CHECK:   func.func @func_loop({{.*}}) attributes {test.block_ids = array<i64: 0, 1, 2, 3>}
 
 // -----
 
@@ -95,16 +257,57 @@ func.func @nested_region(%arg0 : index, %arg1 : index, %arg2 : index) {
   return
 }
 
-// CHECK-LABEL: --- DominanceInfo ---
-// CHECK-NEXT: Nearest(0, 0) = 0
-// CHECK-NEXT: Nearest(0, 1) = 1
+// CHECK: --- DominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 2
 // CHECK: Nearest(1, 0) = 1
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-LABEL: --- PostDominanceInfo ---
-// CHECK-NEXT: Nearest(0, 0) = 0
-// CHECK-NEXT: Nearest(0, 1) = 1
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 2
+// CHECK: Nearest(2, 0) = 2
+// CHECK: Nearest(2, 1) = 2
+// CHECK: Nearest(2, 2) = 2
+
+// CHECK: --- PostDominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 2
 // CHECK: Nearest(1, 0) = 1
-// CHECK-NEXT: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 2
+// CHECK: Nearest(2, 0) = 2
+// CHECK: Nearest(2, 1) = 2
+// CHECK: Nearest(2, 2) = 2
+
+// CHECK: --- Block Dominance relationship ---
+// CHECK: dominates(0, 0) = 1 (properly = 0)
+// CHECK: dominates(0, 1) = 0 (properly = 0)
+// CHECK: dominates(0, 2) = 0 (properly = 0)
+// CHECK: dominates(1, 0) = 1 (properly = 1)
+// CHECK: dominates(1, 1) = 1 (properly = 0)
+// CHECK: dominates(1, 2) = 0 (properly = 0)
+// CHECK: dominates(2, 0) = 1 (properly = 1)
+// CHECK: dominates(2, 1) = 1 (properly = 1)
+// CHECK: dominates(2, 2) = 1 (properly = 1)
+
+// CHECK: --- Block PostDominance relationship ---
+// CHECK: postdominates(0, 0) = 1 (properly = 0)
+// CHECK: postdominates(0, 1) = 0 (properly = 0)
+// CHECK: postdominates(0, 2) = 0 (properly = 0)
+// CHECK: postdominates(1, 0) = 1 (properly = 1)
+// CHECK: postdominates(1, 1) = 1 (properly = 0)
+// CHECK: postdominates(1, 2) = 0 (properly = 0)
+// CHECK: postdominates(2, 0) = 1 (properly = 1)
+// CHECK: postdominates(2, 1) = 1 (properly = 1)
+// CHECK: postdominates(2, 2) = 1 (properly = 1)
+
+// CHECK: module attributes {test.block_ids = array<i64: 2>} {
+// CHECK:   func.func @nested_region({{.*}}) attributes {test.block_ids = array<i64: 1>} {
+// CHECK:     scf.for {{.*}} {
+// CHECK:     } {test.block_ids = array<i64: 0>}
+// CHECK:     return
+// CHECK:   }
+// CHECK: }
 
 // -----
 
@@ -117,32 +320,126 @@ func.func @nested_region2(%arg0 : index, %arg1 : index, %arg2 : index) {
   }
   return
 }
-// CHECK-LABEL: --- DominanceInfo ---
+
+// CHECK: --- DominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 2
+// CHECK: Nearest(0, 3) = 3
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 1
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 2
-// CHECK-NEXT: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 2
+// CHECK: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 2
-// CHECK-NEXT: Nearest(2, 1) = 2
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 1) = 2
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 4) = 4
 // CHECK: Nearest(3, 0) = 3
-// CHECK-NEXT: Nearest(3, 1) = 3
-// CHECK-NEXT: Nearest(3, 2) = 3
-// CHECK-NEXT: Nearest(3, 3) = 3
-// CHECK-LABEL: --- PostDominanceInfo ---
-// CHECK-NEXT: Nearest(0, 0) = 0
-// CHECK-NEXT: Nearest(0, 1) = 1
-// CHECK-NEXT: Nearest(0, 2) = 2
-// CHECK-NEXT: Nearest(0, 3) = 3
+// CHECK: Nearest(3, 1) = 3
+// CHECK: Nearest(3, 2) = 3
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- PostDominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 2
+// CHECK: Nearest(0, 3) = 3
+// CHECK: Nearest(0, 4) = 4
 // CHECK: Nearest(1, 0) = 1
-// CHECK-NEXT: Nearest(1, 1) = 1
-// CHECK-NEXT: Nearest(1, 2) = 2
-// CHECK-NEXT: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 2
+// CHECK: Nearest(1, 3) = 3
+// CHECK: Nearest(1, 4) = 4
 // CHECK: Nearest(2, 0) = 2
-// CHECK-NEXT: Nearest(2, 1) = 2
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 1) = 2
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 3
+// CHECK: Nearest(2, 4) = 4
+// CHECK: Nearest(3, 0) = 3
+// CHECK: Nearest(3, 1) = 3
+// CHECK: Nearest(3, 2) = 3
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(4, 0) = 4
+// CHECK: Nearest(4, 1) = 4
+// CHECK: Nearest(4, 2) = 4
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+
+// CHECK: --- Block Dominance relationship ---
+// CHECK: dominates(0, 0) = 1 (properly = 0)
+// CHECK: dominates(0, 1) = 0 (properly = 0)
+// CHECK: dominates(0, 2) = 0 (properly = 0)
+// CHECK: dominates(0, 3) = 0 (properly = 0)
+// CHECK: dominates(0, 4) = 0 (properly = 0)
+// CHECK: dominates(1, 0) = 1 (properly = 1)
+// CHECK: dominates(1, 1) = 1 (properly = 0)
+// CHECK: dominates(1, 2) = 0 (properly = 0)
+// CHECK: dominates(1, 3) = 0 (properly = 0)
+// CHECK: dominates(1, 4) = 0 (properly = 0)
+// CHECK: dominates(2, 0) = 1 (properly = 1)
+// CHECK: dominates(2, 1) = 1 (properly = 1)
+// CHECK: dominates(2, 2) = 1 (properly = 0)
+// CHECK: dominates(2, 3) = 0 (properly = 0)
+// CHECK: dominates(2, 4) = 0 (properly = 0)
+// CHECK: dominates(3, 0) = 1 (properly = 1)
+// CHECK: dominates(3, 1) = 1 (properly = 1)
+// CHECK: dominates(3, 2) = 1 (properly = 1)
+// CHECK: dominates(3, 3) = 1 (properly = 0)
+// CHECK: dominates(3, 4) = 0 (properly = 0)
+// CHECK: dominates(4, 0) = 1 (properly = 1)
+// CHECK: dominates(4, 1) = 1 (properly = 1)
+// CHECK: dominates(4, 2) = 1 (properly = 1)
+// CHECK: dominates(4, 3) = 1 (properly = 1)
+// CHECK: dominates(4, 4) = 1 (properly = 1)
+
+// CHECK: --- Block PostDominance relationship ---
+// CHECK: postdominates(0, 0) = 1 (properly = 0)
+// CHECK: postdominates(0, 1) = 0 (properly = 0)
+// CHECK: postdominates(0, 2) = 0 (properly = 0)
+// CHECK: postdominates(0, 3) = 0 (properly = 0)
+// CHECK: postdominates(0, 4) = 0 (properly = 0)
+// CHECK: postdominates(1, 0) = 1 (properly = 1)
+// CHECK: postdominates(1, 1) = 1 (properly = 0)
+// CHECK: postdominates(1, 2) = 0 (properly = 0)
+// CHECK: postdominates(1, 3) = 0 (properly = 0)
+// CHECK: postdominates(1, 4) = 0 (properly = 0)
+// CHECK: postdominates(2, 0) = 1 (properly = 1)
+// CHECK: postdominates(2, 1) = 1 (properly = 1)
+// CHECK: postdominates(2, 2) = 1 (properly = 0)
+// CHECK: postdominates(2, 3) = 0 (properly = 0)
+// CHECK: postdominates(2, 4) = 0 (properly = 0)
+// CHECK: postdominates(3, 0) = 1 (properly = 1)
+// CHECK: postdominates(3, 1) = 1 (properly = 1)
+// CHECK: postdominates(3, 2) = 1 (properly = 1)
+// CHECK: postdominates(3, 3) = 1 (properly = 0)
+// CHECK: postdominates(3, 4) = 0 (properly = 0)
+// CHECK: postdominates(4, 0) = 1 (properly = 1)
+// CHECK: postdominates(4, 1) = 1 (properly = 1)
+// CHECK: postdominates(4, 2) = 1 (properly = 1)
+// CHECK: postdominates(4, 3) = 1 (properly = 1)
+// CHECK: postdominates(4, 4) = 1 (properly = 1)
+
+// CHECK: module attributes {test.block_ids = array<i64: 4>} {
+// CHECK:   func.func @nested_region2({{.*}}) attributes {test.block_ids = array<i64: 3>} {
+// CHECK:     scf.for {{.*}} {
+// CHECK:       scf.for {{.*}} {
+// CHECK:         scf.for {{.*}} {
+// CHECK:         } {test.block_ids = array<i64: 0>}
+// CHECK:       } {test.block_ids = array<i64: 1>}
+// CHECK:     } {test.block_ids = array<i64: 2>}
+// CHECK:     return
+// CHECK:   }
+// CHECK: }
 
 // -----
 
@@ -167,141 +464,219 @@ func.func @func_loop_nested_region(
 ^exit:
   return
 }
-// CHECK-LABEL: --- DominanceInfo ---
+
+// CHECK: --- DominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 0
+// CHECK: Nearest(0, 2) = 0
+// CHECK: Nearest(0, 3) = 0
+// CHECK: Nearest(0, 4) = 0
+// CHECK: Nearest(0, 5) = 0
+// CHECK: Nearest(0, 6) = 6
+// CHECK: Nearest(1, 0) = 0
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 1
+// CHECK: Nearest(1, 3) = 1
+// CHECK: Nearest(1, 4) = 1
+// CHECK: Nearest(1, 5) = 1
+// CHECK: Nearest(1, 6) = 6
 // CHECK: Nearest(2, 0) = 0
-// CHECK-NEXT: Nearest(2, 1) = 1
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 2
-// CHECK-NEXT: Nearest(2, 4) = 2
-// CHECK-NEXT: Nearest(2, 5) = 1
+// CHECK: Nearest(2, 1) = 1
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 2
+// CHECK: Nearest(2, 4) = 2
+// CHECK: Nearest(2, 5) = 1
+// CHECK: Nearest(2, 6) = 6
 // CHECK: Nearest(3, 0) = 0
-// CHECK-NEXT: Nearest(3, 1) = 1
-// CHECK-NEXT: Nearest(3, 2) = 2
-// CHECK-NEXT: Nearest(3, 3) = 3
-// CHECK-NEXT: Nearest(3, 4) = 4
-// CHECK-NEXT: Nearest(3, 5) = 1
+// CHECK: Nearest(3, 1) = 1
+// CHECK: Nearest(3, 2) = 2
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(3, 5) = 1
+// CHECK: Nearest(3, 6) = 6
 // CHECK: Nearest(4, 0) = 0
-// CHECK-NEXT: Nearest(4, 1) = 1
-// CHECK-NEXT: Nearest(4, 2) = 2
-// CHECK-NEXT: Nearest(4, 3) = 4
-// CHECK-NEXT: Nearest(4, 4) = 4
-// CHECK-NEXT: Nearest(4, 5) = 1
-// CHECK-LABEL: --- PostDominanceInfo ---
+// CHECK: Nearest(4, 1) = 1
+// CHECK: Nearest(4, 2) = 2
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+// CHECK: Nearest(4, 5) = 1
+// CHECK: Nearest(4, 6) = 6
+// CHECK: Nearest(5, 0) = 0
+// CHECK: Nearest(5, 1) = 1
+// CHECK: Nearest(5, 2) = 1
+// CHECK: Nearest(5, 3) = 1
+// CHECK: Nearest(5, 4) = 1
+// CHECK: Nearest(5, 5) = 5
+// CHECK: Nearest(5, 6) = 6
+// CHECK: Nearest(6, 0) = 6
+// CHECK: Nearest(6, 1) = 6
+// CHECK: Nearest(6, 2) = 6
+// CHECK: Nearest(6, 3) = 6
+// CHECK: Nearest(6, 4) = 6
+// CHECK: Nearest(6, 5) = 6
+// CHECK: Nearest(6, 6) = 6
+
+// CHECK: --- PostDominanceInfo ---
+// CHECK: Nearest(0, 0) = 0
+// CHECK: Nearest(0, 1) = 1
+// CHECK: Nearest(0, 2) = 1
+// CHECK: Nearest(0, 3) = 1
+// CHECK: Nearest(0, 4) = 1
+// CHECK: Nearest(0, 5) = 5
+// CHECK: Nearest(0, 6) = 6
+// CHECK: Nearest(1, 0) = 1
+// CHECK: Nearest(1, 1) = 1
+// CHECK: Nearest(1, 2) = 1
+// CHECK: Nearest(1, 3) = 1
+// CHECK: Nearest(1, 4) = 1
+// CHECK: Nearest(1, 5) = 5
+// CHECK: Nearest(1, 6) = 6
 // CHECK: Nearest(2, 0) = 1
-// CHECK-NEXT: Nearest(2, 1) = 1
-// CHECK-NEXT: Nearest(2, 2) = 2
-// CHECK-NEXT: Nearest(2, 3) = 2
-// CHECK-NEXT: Nearest(2, 4) = 2
-// CHECK-NEXT: Nearest(2, 5) = 5
+// CHECK: Nearest(2, 1) = 1
+// CHECK: Nearest(2, 2) = 2
+// CHECK: Nearest(2, 3) = 2
+// CHECK: Nearest(2, 4) = 2
+// CHECK: Nearest(2, 5) = 5
+// CHECK: Nearest(2, 6) = 6
 // CHECK: Nearest(3, 0) = 1
-// CHECK-NEXT: Nearest(3, 1) = 1
-// CHECK-NEXT: Nearest(3, 2) = 2
-// CHECK-NEXT: Nearest(3, 3) = 3
-// CHECK-NEXT: Nearest(3, 4) = 4
-// CHECK-NEXT: Nearest(3, 5) = 5
+// CHECK: Nearest(3, 1) = 1
+// CHECK: Nearest(3, 2) = 2
+// CHECK: Nearest(3, 3) = 3
+// CHECK: Nearest(3, 4) = 4
+// CHECK: Nearest(3, 5) = 5
+// CHECK: Nearest(3, 6) = 6
 // CHECK: Nearest(4, 0) = 1
-// CHECK-NEXT: Nearest(4, 1) = 1
-// CHECK-NEXT: Nearest(4, 2) = 2
-// CHECK-NEXT: Nearest(4, 3) = 4
-// CHECK-NEXT: Nearest(4, 4) = 4
-// CHECK-NEXT: Nearest(4, 5) = 5
-// CHECK-LABEL: --- Block Dominance relationship ---
-// CHECK-NEXT: dominates(0, 0) = true
-// CHECK-NEXT: dominates(0, 1) = true
-// CHECK-NEXT: dominates(0, 2) = true
-// CHECK-NEXT: dominates(0, 3) = true
-// CHECK-NEXT: dominates(0, 4) = true
-// CHECK-NEXT: dominates(0, 5) = true
-// CHECK-NEXT: dominates(0, 6) = false
-// CHECK-NEXT: dominates(1, 0) = false
-// CHECK-NEXT: dominates(1, 1) = true
-// CHECK-NEXT: dominates(1, 2) = true
-// CHECK-NEXT: dominates(1, 3) = true
-// CHECK-NEXT: dominates(1, 4) = true
-// CHECK-NEXT: dominates(1, 5) = true
-// CHECK-NEXT: dominates(1, 6) = false
-// CHECK-NEXT: dominates(2, 0) = false
-// CHECK-NEXT: dominates(2, 1) = false
-// CHECK-NEXT: dominates(2, 2) = true
-// CHECK-NEXT: dominates(2, 3) = true
-// CHECK-NEXT: dominates(2, 4) = true
-// CHECK-NEXT: dominates(2, 5) = false
-// CHECK-NEXT: dominates(2, 6) = false
-// CHECK-NEXT: dominates(3, 0) = false
-// CHECK-NEXT: dominates(3, 1) = false
-// CHECK-NEXT: dominates(3, 2) = false
-// CHECK-NEXT: dominates(3, 3) = true
-// CHECK-NEXT: dominates(3, 4) = false
-// CHECK-NEXT: dominates(3, 5) = false
-// CHECK-NEXT: dominates(3, 6) = false
-// CHECK-NEXT: dominates(4, 0) = false
-// CHECK-NEXT: dominates(4, 1) = false
-// CHECK-NEXT: dominates(4, 2) = false
-// CHECK-NEXT: dominates(4, 3) = true
-// CHECK-NEXT: dominates(4, 4) = true
-// CHECK-NEXT: dominates(4, 5) = false
-// CHECK-NEXT: dominates(4, 6) = false
-// CHECK-NEXT: dominates(5, 0) = false
-// CHECK-NEXT: dominates(5, 1) = false
-// CHECK-NEXT: dominates(5, 2) = false
-// CHECK-NEXT: dominates(5, 3) = false
-// CHECK-NEXT: dominates(5, 4) = false
-// CHECK-NEXT: dominates(5, 5) = true
-// CHECK-NEXT: dominates(5, 6) = false
-// CHECK-NEXT: dominates(6, 0) = true
-// CHECK-NEXT: dominates(6, 1) = true
-// CHECK-NEXT: dominates(6, 2) = true
-// CHECK-NEXT: dominates(6, 3) = true
-// CHECK-NEXT: dominates(6, 4) = true
-// CHECK-NEXT: dominates(6, 5) = true
-// CHECK-NEXT: dominates(6, 6) = true
-// CHECK-LABEL: --- Block PostDominance relationship ---
-// CHECK-NEXT: postdominates(0, 0) = true
-// CHECK-NEXT: postdominates(0, 1) = false
-// CHECK-NEXT: postdominates(0, 2) = false
-// CHECK-NEXT: postdominates(0, 3) = false
-// CHECK-NEXT: postdominates(0, 4) = false
-// CHECK-NEXT: postdominates(0, 5) = false
-// CHECK-NEXT: postdominates(0, 6) = false
-// CHECK-NEXT: postdominates(1, 0) = true
-// CHECK-NEXT: postdominates(1, 1) = true
-// CHECK-NEXT: postdominates(1, 2) = true
-// CHECK-NEXT: postdominates(1, 3) = true
-// CHECK-NEXT: postdominates(1, 4) = true
-// CHECK-NEXT: postdominates(1, 5) = false
-// CHECK-NEXT: postdominates(1, 6) = false
-// CHECK-NEXT: postdominates(2, 0) = false
-// CHECK-NEXT: postdominates(2, 1) = false
-// CHECK-NEXT: postdominates(2, 2) = true
-// CHECK-NEXT: postdominates(2, 3) = true
-// CHECK-NEXT: postdominates(2, 4) = true
-// CHECK-NEXT: postdominates(2, 5) = false
-// CHECK-NEXT: postdominates(2, 6) = false
-// CHECK-NEXT: postdominates(3, 0) = false
-// CHECK-NEXT: postdominates(3, 1) = false
-// CHECK-NEXT: postdominates(3, 2) = false
-// CHECK-NEXT: postdominates(3, 3) = true
-// CHECK-NEXT: postdominates(3, 4) = false
-// CHECK-NEXT: postdominates(3, 5) = false
-// CHECK-NEXT: postdominates(3, 6) = false
-// CHECK-NEXT: postdominates(4, 0) = false
-// CHECK-NEXT: postdominates(4, 1) = false
-// CHECK-NEXT: postdominates(4, 2) = false
-// CHECK-NEXT: postdominates(4, 3) = true
-// CHECK-NEXT: postdominates(4, 4) = true
-// CHECK-NEXT: postdominates(4, 5) = false
-// CHECK-NEXT: postdominates(4, 6) = false
-// CHECK-NEXT: postdominates(5, 0) = true
-// CHECK-NEXT: postdominates(5, 1) = true
-// CHECK-NEXT: postdominates(5, 2) = true
-// CHECK-NEXT: postdominates(5, 3) = true
-// CHECK-NEXT: postdominates(5, 4) = true
-// CHECK-NEXT: postdominates(5, 5) = true
-// CHECK-NEXT: postdominates(5, 6) = false
-// CHECK-NEXT: postdominates(6, 0) = true
-// CHECK-NEXT: postdominates(6, 1) = true
-// CHECK-NEXT: postdominates(6, 2) = true
-// CHECK-NEXT: postdominates(6, 3) = true
-// CHECK-NEXT: postdominates(6, 4) = true
-// CHECK-NEXT: postdominates(6, 5) = true
-// CHECK-NEXT: postdominates(6, 6) = true
+// CHECK: Nearest(4, 1) = 1
+// CHECK: Nearest(4, 2) = 2
+// CHECK: Nearest(4, 3) = 4
+// CHECK: Nearest(4, 4) = 4
+// CHECK: Nearest(4, 5) = 5
+// CHECK: Nearest(4, 6) = 6
+// CHECK: Nearest(5, 0) = 5
+// CHECK: Nearest(5, 1) = 5
+// CHECK: Nearest(5, 2) = 5
+// CHECK: Nearest(5, 3) = 5
+// CHECK: Nearest(5, 4) = 5
+// CHECK: Nearest(5, 5) = 5
+// CHECK: Nearest(5, 6) = 6
+// CHECK: Nearest(6, 0) = 6
+// CHECK: Nearest(6, 1) = 6
+// CHECK: Nearest(6, 2) = 6
+// CHECK: Nearest(6, 3) = 6
+// CHECK: Nearest(6, 4) = 6
+// CHECK: Nearest(6, 5) = 6
+// CHECK: Nearest(6, 6) = 6
+
+// CHECK: --- Block Dominance relationship ---
+// CHECK: dominates(0, 0) = 1 (properly = 0)
+// CHECK: dominates(0, 1) = 1 (properly = 1)
+// CHECK: dominates(0, 2) = 1 (properly = 1)
+// CHECK: dominates(0, 3) = 1 (properly = 1)
+// CHECK: dominates(0, 4) = 1 (properly = 1)
+// CHECK: dominates(0, 5) = 1 (properly = 1)
+// CHECK: dominates(0, 6) = 0 (properly = 0)
+// CHECK: dominates(1, 0) = 0 (properly = 0)
+// CHECK: dominates(1, 1) = 1 (properly = 0)
+// CHECK: dominates(1, 2) = 1 (properly = 1)
+// CHECK: dominates(1, 3) = 1 (properly = 1)
+// CHECK: dominates(1, 4) = 1 (properly = 1)
+// CHECK: dominates(1, 5) = 1 (properly = 1)
+// CHECK: dominates(1, 6) = 0 (properly = 0)
+// CHECK: dominates(2, 0) = 0 (properly = 0)
+// CHECK: dominates(2, 1) = 0 (properly = 0)
+// CHECK: dominates(2, 2) = 1 (properly = 0)
+// CHECK: dominates(2, 3) = 1 (properly = 1)
+// CHECK: dominates(2, 4) = 1 (properly = 1)
+// CHECK: dominates(2, 5) = 0 (properly = 0)
+// CHECK: dominates(2, 6) = 0 (properly = 0)
+// CHECK: dominates(3, 0) = 0 (properly = 0)
+// CHECK: dominates(3, 1) = 0 (properly = 0)
+// CHECK: dominates(3, 2) = 0 (properly = 0)
+// CHECK: dominates(3, 3) = 1 (properly = 0)
+// CHECK: dominates(3, 4) = 0 (properly = 0)
+// CHECK: dominates(3, 5) = 0 (properly = 0)
+// CHECK: dominates(3, 6) = 0 (properly = 0)
+// CHECK: dominates(4, 0) = 0 (properly = 0)
+// CHECK: dominates(4, 1) = 0 (properly = 0)
+// CHECK: dominates(4, 2) = 0 (properly = 0)
+// CHECK: dominates(4, 3) = 1 (properly = 1)
+// CHECK: dominates(4, 4) = 1 (properly = 0)
+// CHECK: dominates(4, 5) = 0 (properly = 0)
+// CHECK: dominates(4, 6) = 0 (properly = 0)
+// CHECK: dominates(5, 0) = 0 (properly = 0)
+// CHECK: dominates(5, 1) = 0 (properly = 0)
+// CHECK: dominates(5, 2) = 0 (properly = 0)
+// CHECK: dominates(5, 3) = 0 (properly = 0)
+// CHECK: dominates(5, 4) = 0 (properly = 0)
+// CHECK: dominates(5, 5) = 1 (properly = 0)
+// CHECK: dominates(5, 6) = 0 (properly = 0)
+// CHECK: dominates(6, 0) = 1 (properly = 1)
+// CHECK: dominates(6, 1) = 1 (properly = 1)
+// CHECK: dominates(6, 2) = 1 (properly = 1)
+// CHECK: dominates(6, 3) = 1 (properly = 1)
+// CHECK: dominates(6, 4) = 1 (properly = 1)
+// CHECK: dominates(6, 5) = 1 (properly = 1)
+// CHECK: dominates(6, 6) = 1 (properly = 1)
+
+// CHECK: --- Block PostDominance relationship ---
+// CHECK: postdominates(0, 0) = 1 (properly = 0)
+// CHECK: postdominates(0, 1) = 0 (properly = 0)
+// CHECK: postdominates(0, 2) = 0 (properly = 0)
+// CHECK: postdominates(0, 3) = 0 (properly = 0)
+// CHECK: postdominates(0, 4) = 0 (properly = 0)
+// CHECK: postdominates(0, 5) = 0 (properly = 0)
+// CHECK: postdominates(0, 6) = 0 (properly = 0)
+// CHECK: postdominates(1, 0) = 1 (properly = 1)
+// CHECK: postdominates(1, 1) = 1 (properly = 0)
+// CHECK: postdominates(1, 2) = 1 (properly = 1)
+// CHECK: postdominates(1, 3) = 1 (properly = 1)
+// CHECK: postdominates(1, 4) = 1 (properly = 1)
+// CHECK: postdominates(1, 5) = 0 (properly = 0)
+// CHECK: postdominates(1, 6) = 0 (properly = 0)
+// CHECK: postdominates(2, 0) = 0 (properly = 0)
+// CHECK: postdominates(2, 1) = 0 (properly = 0)
+// CHECK: postdominates(2, 2) = 1 (properly = 0)
+// CHECK: postdominates(2, 3) = 1 (properly = 1)
+// CHECK: postdominates(2, 4) = 1 (properly = 1)
+// CHECK: postdominates(2, 5) = 0 (properly = 0)
+// CHECK: postdominates(2, 6) = 0 (properly = 0)
+// CHECK: postdominates(3, 0) = 0 (properly = 0)
+// CHECK: postdominates(3, 1) = 0 (properly = 0)
+// CHECK: postdominates(3, 2) = 0 (properly = 0)
+// CHECK: postdominates(3, 3) = 1 (properly = 0)
+// CHECK: postdominates(3, 4) = 0 (properly = 0)
+// CHECK: postdominates(3, 5) = 0 (properly = 0)
+// CHECK: postdominates(3, 6) = 0 (properly = 0)
+// CHECK: postdominates(4, 0) = 0 (properly = 0)
+// CHECK: postdominates(4, 1) = 0 (properly = 0)
+// CHECK: postdominates(4, 2) = 0 (properly = 0)
+// CHECK: postdominates(4, 3) = 1 (properly = 1)
+// CHECK: postdominates(4, 4) = 1 (properly = 0)
+// CHECK: postdominates(4, 5) = 0 (properly = 0)
+// CHECK: postdominates(4, 6) = 0 (properly = 0)
+// CHECK: postdominates(5, 0) = 1 (properly = 1)
+// CHECK: postdominates(5, 1) = 1 (properly = 1)
+// CHECK: postdominates(5, 2) = 1 (properly = 1)
+// CHECK: postdominates(5, 3) = 1 (properly = 1)
+// CHECK: postdominates(5, 4) = 1 (properly = 1)
+// CHECK: postdominates(5, 5) = 1 (properly = 0)
+// CHECK: postdominates(5, 6) = 0 (properly = 0)
+// CHECK: postdominates(6, 0) = 1 (properly = 1)
+// CHECK: postdominates(6, 1) = 1 (properly = 1)
+// CHECK: postdominates(6, 2) = 1 (properly = 1)
+// CHECK: postdominates(6, 3) = 1 (properly = 1)
+// CHECK: postdominates(6, 4) = 1 (properly = 1)
+// CHECK: postdominates(6, 5) = 1 (properly = 1)
+// CHECK: postdominates(6, 6) = 1 (properly = 1)
+
+// CHECK: module attributes {test.block_ids = array<i64: 6>} {
+// CHECK:   func.func @func_loop_nested_region({{.*}}) attributes {test.block_ids = array<i64: 0, 1, 2, 5>} {
+// CHECK:   ^{{.*}}
+// CHECK:   ^{{.*}}
+// CHECK:     scf.for {{.*}} {
+// CHECK:       scf.for {{.*}} {
+// CHECK:       } {test.block_ids = array<i64: 3>}
+// CHECK:     } {test.block_ids = array<i64: 4>}
+// CHECK:   ^{{.*}}
+// CHECK:   }
+// CHECK: }
diff --git a/mlir/test/lib/IR/TestDominance.cpp b/mlir/test/lib/IR/TestDominance.cpp
index fab80bdacb032..b34149b3e2cbd 100644
--- a/mlir/test/lib/IR/TestDominance.cpp
+++ b/mlir/test/lib/IR/TestDominance.cpp
@@ -12,6 +12,7 @@
 //
 //===----------------------------------------------------------------------===//
 
+#include "mlir/IR/Builders.h"
 #include "mlir/IR/Dominance.h"
 #include "mlir/IR/SymbolTable.h"
 #include "mlir/Pass/Pass.h"
@@ -24,24 +25,46 @@ static bool dominatesOrPostDominates(DominanceInfo &dominanceInfo, Block *a,
                                      Block *b) {
   return dominanceInfo.dominates(a, b);
 }
-
 static bool dominatesOrPostDominates(PostDominanceInfo &dominanceInfo, Block *a,
                                      Block *b) {
   return dominanceInfo.postDominates(a, b);
 }
+static bool properlyDominatesOrPostDominates(DominanceInfo &dominanceInfo,
+                                             Block *a, Block *b) {
+  return dominanceInfo.properlyDominates(a, b);
+}
+static bool properlyDominatesOrPostDominates(PostDominanceInfo &dominanceInfo,
+                                             Block *a, Block *b) {
+  return dominanceInfo.properlyPostDominates(a, b);
+}
 
 namespace {
 
 /// Helper class to print dominance information.
 class DominanceTest {
 public:
+  static constexpr StringRef kBlockIdsAttrName = "test.block_ids";
+
   /// Constructs a new test instance using the given operation.
   DominanceTest(Operation *operation) : operation(operation) {
-    // Create unique ids for each block.
+    Builder b(operation->getContext());
+
+    // Helper function that annotates the IR with block IDs.
+    auto annotateBlockId = [&](Operation *op, int64_t blockId) {
+      auto idAttr = op->getAttrOfType<DenseI64ArrayAttr>(kBlockIdsAttrName);
+      SmallVector<int64_t> ids;
+      if (idAttr)
+        ids = llvm::to_vector(idAttr.asArrayRef());
+      ids.push_back(blockId);
+      op->setAttr(kBlockIdsAttrName, b.getDenseI64ArrayAttr(ids));
+    };
+
+    // Create unique IDs for each block.
     operation->walk([&](Operation *nested) {
       if (blockIds.count(nested->getBlock()) > 0)
         return;
       blockIds.insert({nested->getBlock(), blockIds.size()});
+      annotateBlockId(nested->getBlock()->getParentOp(), blockIds.size() - 1);
     });
   }
 
@@ -61,26 +84,28 @@ class DominanceTest {
         if (!visited.insert(nestedBlock).second)
           return;
         if (printCommonDominatorInfo) {
-          llvm::errs() << "Nearest(" << blockIds[block] << ", "
+          llvm::outs() << "Nearest(" << blockIds[block] << ", "
                        << blockIds[nestedBlock] << ") = ";
           Block *dom =
               dominanceInfo.findNearestCommonDominator(block, nestedBlock);
           if (dom)
-            llvm::errs() << blockIds[dom];
+            llvm::outs() << blockIds[dom];
           else
-            llvm::errs() << "<no dom>";
-          llvm::errs() << "\n";
+            llvm::outs() << "<no dom>";
+          llvm::outs() << "\n";
         } else {
           if (std::is_same<DominanceInfo, DominanceT>::value)
-            llvm::errs() << "dominates(";
-          else
-            llvm::errs() << "postdominates(";
-          llvm::errs() << blockIds[block] << ", " << blockIds[nestedBlock]
-                       << ") = ";
-          if (dominatesOrPostDominates(dominanceInfo, block, nestedBlock))
-            llvm::errs() << "true\n";
+            llvm::outs() << "dominates(";
           else
-            llvm::errs() << "false\n";
+            llvm::outs() << "postdominates(";
+          llvm::outs() << blockIds[block] << ", " << blockIds[nestedBlock]
+                       << ") = "
+                       << std::to_string(dominatesOrPostDominates(
+                              dominanceInfo, block, nestedBlock))
+                       << " (properly = "
+                       << std::to_string(properlyDominatesOrPostDominates(
+                              dominanceInfo, block, nestedBlock))
+                       << ")\n";
         }
       });
     });
@@ -101,24 +126,24 @@ struct TestDominancePass
   }
 
   void runOnOperation() override {
-    llvm::errs() << "Testing : " << getOperation().getName() << "\n";
+    llvm::outs() << "Testing : " << getOperation().getName() << "\n";
     DominanceTest dominanceTest(getOperation());
 
     // Print dominance information.
-    llvm::errs() << "--- DominanceInfo ---\n";
+    llvm::outs() << "--- DominanceInfo ---\n";
     dominanceTest.printDominance(getAnalysis<DominanceInfo>(),
                                  /*printCommonDominatorInfo=*/true);
 
-    llvm::errs() << "--- PostDominanceInfo ---\n";
+    llvm::outs() << "--- PostDominanceInfo ---\n";
     dominanceTest.printDominance(getAnalysis<PostDominanceInfo>(),
                                  /*printCommonDominatorInfo=*/true);
 
     // Print dominance relationship between blocks.
-    llvm::errs() << "--- Block Dominance relationship ---\n";
+    llvm::outs() << "--- Block Dominance relationship ---\n";
     dominanceTest.printDominance(getAnalysis<DominanceInfo>(),
                                  /*printCommonDominatorInfo=*/false);
 
-    llvm::errs() << "--- Block PostDominance relationship ---\n";
+    llvm::outs() << "--- Block PostDominance relationship ---\n";
     dominanceTest.printDominance(getAnalysis<PostDominanceInfo>(),
                                  /*printCommonDominatorInfo=*/false);
   }