RundownTaskCounter needs to use a non-nestable task to block on the completion of already scheduled…

chrome/browser/browser_process_impl.cc

Index: chrome/browser/browser_process_impl.cc
diff --git a/chrome/browser/browser_process_impl.cc b/chrome/browser/browser_process_impl.cc
index 01cac71b8f0858ec7963941690669f68e81170d2..34b25146884cc31b30c0e86f7938eb9c84a95f2f 100644
--- a/chrome/browser/browser_process_impl.cc
+++ b/chrome/browser/browser_process_impl.cc
@@ -426,7 +426,9 @@ void RundownTaskCounter::Post(base::SequencedTaskRunner* task_runner) {
 
   base::AtomicRefCountInc(&count_);
 
-  task_runner->PostTask(FROM_HERE,
+  // The task must be non-nestable to guarantee that it runs after all tasks
+  // currently scheduled on |task_runner| have completed.
+  task_runner->PostNonNestableTask(FROM_HERE,
       base::Bind(&RundownTaskCounter::Decrement, this));
 }