// the equation "abc,cd->ad".
  absl::btree_set<char> reduced_label_set(input_subs.begin(), input_subs.end());
  for (const char x : output_subs) {
    reduced_label_set.erase(x);
  }
  for (const char x : other_subs) {
    reduced_label_set.erase(x);
  }
  reduced_label_set.erase('.');

  // Obtain the input subscripts with the reduced axis labels removed. E.g.