diff --git a/src/op/parallel.cc b/src/op/parallel.cc
index 7a82a101d..5fa90ba95 100644
--- a/src/op/parallel.cc
+++ b/src/op/parallel.cc
@@ -53,15 +53,18 @@ bool ProveFragmentContains(Fragment small_frag, Fragment large_frag,
   // (forward index) of both fragments are equal. This is required when
   // validating loop layout against buffer fragment, as code generation
   // needs to correctly derive buffer physical indices from loop layout.
+  bool large_physical_is_fully_replicated = large_frag->IsCompletedReplicated();
+  if (large_physical_is_fully_replicated) {
+    return true; // fully replicated fragments are always compatible
+  }
+
   if (check_forward_index) {
     auto small_physical = small_frag->Forward(small_frag_indices);
     auto large_physical = large_frag->Forward(large_frag_indices);
-
     // Dimension mismatch means they are not equal.
     if (small_physical.size() != large_physical.size()) {
       return false;
     }
-
     // Check each physical index component for equality.
     for (size_t i = 0; i < small_physical.size(); i++) {
       auto diff = analyzer_.Simplify(small_physical[i] - large_physical[i]);
@@ -649,7 +652,7 @@ bool ParallelOpNode::ValidateCandidateAgainstFragments(
     // check_forward_index=true: when validating loop layout against buffer
     // fragment, we need to ensure physical indices match for correct code gen.
     if (!ProveFragmentContains(candidate, fragment, vars, indice_map_[buffer],
-                               analyzer_)) {
+                               analyzer_, /*check_forward_index=*/true)) {
       return false;
     }
   }
@@ -815,8 +818,7 @@ ParallelOpNode::ChooseBestCandidate(const Fragment &candidate_from_buffer,
   auto contains = [&](const Fragment &big, const Fragment &small) {
     // contains(A, B) means: for any loop index, the threads that access
     // B's elements are a subset of those that access A's elements.
-    return ProveFragmentContains(small, big, vars, vars, analyzer_,
-                                 /*check_forward_index=*/true);
+    return ProveFragmentContains(small, big, vars, vars, analyzer_);
   };
 
   bool buf_ok = ValidateCandidateAgainstFragments(candidate_from_buffer, T);