  We prove that all valid Herbrand equalities can be inter-procedurally
inferred for programs where all assignments whose right-hand sides depend on at
most one variable are taken into account. The analysis is based on procedure
summaries representing the weakest pre-conditions for finitely many generic
post-conditions with template variables. In order to arrive at effective
representations for all occurring weakest pre-conditions, we show for almost
all values possibly computed at run-time, that they can be uniquely factorized
into tree patterns and a ground term. Moreover, we introduce an approximate
notion of subsumption which is effectively decidable and ensures that finite
conjunctions of equalities may not grow infinitely. Based on these technical
results, we realize an effective fixpoint iteration to infer all
inter-procedurally valid Herbrand equalities for these programs. Finally we
show that an invariant candidate with a constant number of variables, can be
verified in polynomial time.
