  There are termination proofs that are produced by termination tools for which
certifiers are not powerful enough. However, a similar situation also occurs in
the other direction. We have formalized termination techniques in a more
general setting as they have been introduced. Hence, we can certify proofs
using techniques that no termination tool supports so far. In this paper we
shortly present two of these formalizations: Polynomial orders with negative
constants and Arctic termination.
