Index: lib/Analysis/ScalarEvolution.cpp
===================================================================
--- lib/Analysis/ScalarEvolution.cpp
+++ lib/Analysis/ScalarEvolution.cpp
@@ -9100,6 +9100,25 @@
       return true;
   }
 
+  // If we cannot prove strict comparison (e.g. a > b), maybe we can prove
+  // the facts (a >= b && a != b) separately. A typical situation is when the
+  // non-strict comparison is known from ranges and non-equality is known from
+  // dominating predicates.
+  auto LoosePredicate = [](ICmpInst::Predicate Pred) {
+    switch (Pred) {
+    case ICmpInst::ICMP_SGT: return ICmpInst::ICMP_SGE;
+    case ICmpInst::ICMP_SLT: return ICmpInst::ICMP_SLE;
+    case ICmpInst::ICMP_UGT: return ICmpInst::ICMP_UGE;
+    case ICmpInst::ICMP_ULT: return ICmpInst::ICMP_ULE;
+    default: return Pred;
+    }
+  };
+  auto NonStrictPredicate = LoosePredicate(Pred);
+  if (Pred != NonStrictPredicate &&
+      isLoopEntryGuardedByCond(L, ICmpInst::ICMP_NE, LHS, RHS) &&
+      isLoopEntryGuardedByCond(L, NonStrictPredicate, LHS, RHS))
+    return true;
+
   return false;
 }
 
Index: test/Transforms/IRCE/conjunctive-checks.ll
===================================================================
--- test/Transforms/IRCE/conjunctive-checks.ll
+++ test/Transforms/IRCE/conjunctive-checks.ll
@@ -4,10 +4,10 @@
 ; CHECK-LABEL: @f_0(
 
 ; CHECK: loop.preheader:
-; CHECK: [[not_n:[^ ]+]] = sub i32 -1, %n
 ; CHECK: [[not_safe_range_end:[^ ]+]] = sub i32 3, %len
-; CHECK: [[not_exit_main_loop_at_hiclamp_cmp:[^ ]+]] = icmp sgt i32 [[not_n]], [[not_safe_range_end]]
-; CHECK: [[not_exit_main_loop_at_hiclamp:[^ ]+]] = select i1 [[not_exit_main_loop_at_hiclamp_cmp]], i32 [[not_n]], i32 [[not_safe_range_end]]
+; CHECK: [[not_n:[^ ]+]] = sub i32 -1, %n
+; CHECK: [[not_exit_main_loop_at_hiclamp_cmp:[^ ]+]] = icmp sgt i32 [[not_safe_range_end]], [[not_n]]
+; CHECK: [[not_exit_main_loop_at_hiclamp:[^ ]+]] = select i1 [[not_exit_main_loop_at_hiclamp_cmp]], i32 [[not_safe_range_end]], i32 [[not_n]]
 ; CHECK: [[exit_main_loop_at_hiclamp:[^ ]+]] = sub i32 -1, [[not_exit_main_loop_at_hiclamp]]
 ; CHECK: [[exit_main_loop_at_loclamp_cmp:[^ ]+]] = icmp sgt i32 [[exit_main_loop_at_hiclamp]], 0
 ; CHECK: [[exit_main_loop_at_loclamp:[^ ]+]] = select i1 [[exit_main_loop_at_loclamp_cmp]], i32 [[exit_main_loop_at_hiclamp]], i32 0
Index: test/Transforms/IRCE/decrementing-loop.ll
===================================================================
--- test/Transforms/IRCE/decrementing-loop.ll
+++ test/Transforms/IRCE/decrementing-loop.ll
@@ -1,4 +1,8 @@
-; RUN: opt -verify-loop-info -irce -S < %s | FileCheck %s
+; RUN: opt -verify-loop-info -irce -debug-only=irce -S < %s 2>&1 | FileCheck %s
+
+; CHECK-LABEL: irce: in function decrementing_loop: constrained Loop at depth 1
+; CHECK-LABEL: irce: in function test_01: constrained Loop at depth 1
+; CHECK-LABEL: irce: in function test_02: constrained Loop at depth 1
 
 define void @decrementing_loop(i32 *%arr, i32 *%a_len_ptr, i32 %n) {
  entry:
@@ -38,5 +42,85 @@
 ; CHECK:   %exit.preloop.at = add i32 [[not_exit_preloop_at]], -1
 }
 
+; Make sure that we can eliminate the range check when the loop looks like:
+; for (i = len.a - 1; i >= 0; --i)
+;   b[i] = a[i];
+define void @test_01(i32* %a, i32* %b, i32* %a_len_ptr, i32* %b_len_ptr) {
+
+; CHECK-LABEL: test_01
+; CHECK:       mainloop:
+; CHECK-NEXT:    br label %loop
+; CHECK:       loop:
+; CHECK:         %rc = and i1 true, true
+; CHECK:       loop.preloop:
+
+ entry:
+  %len.a = load i32, i32* %a_len_ptr, !range !0
+  %len.b = load i32, i32* %b_len_ptr, !range !0
+  %first.itr.check = icmp ne i32 %len.a, 0
+  br i1 %first.itr.check, label %loop, label %exit
+
+ loop:
+  %idx = phi i32 [ %len.a, %entry ] , [ %idx.next, %in.bounds ]
+  %idx.next = sub i32 %idx, 1
+  %rca = icmp ult i32 %idx.next, %len.a
+  %rcb = icmp ult i32 %idx.next, %len.b
+  %rc = and i1 %rca, %rcb
+  br i1 %rc, label %in.bounds, label %out.of.bounds, !prof !1
+
+ in.bounds:
+  %el.a = getelementptr i32, i32* %a, i32 %idx.next
+  %el.b = getelementptr i32, i32* %b, i32 %idx.next
+  %v = load i32, i32* %el.a
+  store i32 %v, i32* %el.b
+  %loop.cond = icmp slt i32 %idx, 2
+  br i1 %loop.cond, label %exit, label %loop
+
+ out.of.bounds:
+  ret void
+
+ exit:
+  ret void
+}
+
+; Same as test_01, but the latch condition is unsigned
+define void @test_02(i32* %a, i32* %b, i32* %a_len_ptr, i32* %b_len_ptr) {
+
+; CHECK-LABEL: test_02
+; CHECK:       mainloop:
+; CHECK-NEXT:    br label %loop
+; CHECK:       loop:
+; CHECK:         %rc = and i1 true, true
+; CHECK:       loop.preloop:
+
+ entry:
+  %len.a = load i32, i32* %a_len_ptr, !range !0
+  %len.b = load i32, i32* %b_len_ptr, !range !0
+  %first.itr.check = icmp ne i32 %len.a, 0
+  br i1 %first.itr.check, label %loop, label %exit
+
+ loop:
+  %idx = phi i32 [ %len.a, %entry ] , [ %idx.next, %in.bounds ]
+  %idx.next = sub i32 %idx, 1
+  %rca = icmp ult i32 %idx.next, %len.a
+  %rcb = icmp ult i32 %idx.next, %len.b
+  %rc = and i1 %rca, %rcb
+  br i1 %rc, label %in.bounds, label %out.of.bounds, !prof !1
+
+ in.bounds:
+  %el.a = getelementptr i32, i32* %a, i32 %idx.next
+  %el.b = getelementptr i32, i32* %b, i32 %idx.next
+  %v = load i32, i32* %el.a
+  store i32 %v, i32* %el.b
+  %loop.cond = icmp ult i32 %idx, 2
+  br i1 %loop.cond, label %exit, label %loop
+
+ out.of.bounds:
+  ret void
+
+ exit:
+  ret void
+}
+
 !0 = !{i32 0, i32 2147483647}
 !1 = !{!"branch_weights", i32 64, i32 4}
Index: test/Transforms/IRCE/single-access-no-preloop.ll
===================================================================
--- test/Transforms/IRCE/single-access-no-preloop.ll
+++ test/Transforms/IRCE/single-access-no-preloop.ll
@@ -85,10 +85,10 @@
 ; CHECK-LABEL: @single_access_no_preloop_with_offset(
 
 ; CHECK: loop.preheader:
-; CHECK: [[not_n:[^ ]+]] = sub i32 -1, %n
 ; CHECK: [[not_safe_range_end:[^ ]+]] = sub i32 3, %len
-; CHECK: [[not_exit_main_loop_at_hiclamp_cmp:[^ ]+]] = icmp sgt i32 [[not_n]], [[not_safe_range_end]]
-; CHECK: [[not_exit_main_loop_at_hiclamp:[^ ]+]] = select i1 [[not_exit_main_loop_at_hiclamp_cmp]], i32 [[not_n]], i32 [[not_safe_range_end]]
+; CHECK: [[not_n:[^ ]+]] = sub i32 -1, %n
+; CHECK: [[not_exit_main_loop_at_hiclamp_cmp:[^ ]+]] = icmp sgt i32 [[not_safe_range_end]], [[not_n]]
+; CHECK: [[not_exit_main_loop_at_hiclamp:[^ ]+]] = select i1 [[not_exit_main_loop_at_hiclamp_cmp]], i32 [[not_safe_range_end]], i32 [[not_n]]
 ; CHECK: [[exit_main_loop_at_hiclamp:[^ ]+]] = sub i32 -1, [[not_exit_main_loop_at_hiclamp]]
 ; CHECK: [[exit_main_loop_at_loclamp_cmp:[^ ]+]] = icmp sgt i32 [[exit_main_loop_at_hiclamp]], 0
 ; CHECK: [[exit_main_loop_at_loclamp:[^ ]+]] = select i1 [[exit_main_loop_at_loclamp_cmp]], i32 [[exit_main_loop_at_hiclamp]], i32 0