  We investigate the relationship between two independently developed
termination techniques. On the one hand, sized-types based termination (SBT)
uses types annotated with size expressions and Girard's reducibility
candidates, and applies on systems using constructor matching only. On the
other hand, semantic labelling transforms a rewrite system by annotating each
function symbol with the semantics of its arguments, and applies to any rewrite
system. First, we introduce a simplified version of SBT for the simply-typed
lambda-calculus. Then, we give new proofs of the correctness of SBT using
semantic labelling, both in the first and in the higher-order case. As a
consequence, we show that SBT can be extended to systems using matching on
defined symbols (e.g. associative functions).
