This paper introduces an important relation defined on the set of all traversals of derivation trees. Since algorithms adopt different ways of traversing derivation trees for any linguistic construct, it is a critical problem to be able to determine which of those traversals could be considered as equivalent. The same-to-a-subtree (STAS) relation does this, dividing the universe of all legal traversals of a given tree into equivalence classes. Its usefulness and applicability to the evaluation of linguistic grammar processing (parsing or generation) algorithms is endorsed. It is shown that covering more equivalence classes by an algorithm, means more complete and more reversible algorithm. We also demonstrate usefulness and applicability of STAS relation on an example of comparing semantic-head-driven generation algorithm and essential arguments algorithm.