// All the lhs equations should come first.
  if (lhs_out_idx_end > rhs_out_idx_start) return false;

  // All the lhs out dim and rhs out dim should be larger than the batch dims,
  // and they should not be mixed.
  int batch_dim_size = std::max(rhs_batch_dim_size, lhs_batch_dim_size);
  return lhs_out_idx_start >= batch_dim_size &&
         rhs_out_idx_start >= batch_dim_size;
}