  Given any K and N we show that there exists a compact geodesic metric measure
space satisfying locally the CD(0,4) condition but failing CD(K,N) globally.
The space with this property is a suitable non convex subset of R^2 equipped
with the l^\infty-norm and the Lebesgue measure. Combining many such spaces
gives a (non compact) complete geodesic metric measure space satisfying CD(0,4)
locally but failing CD(K,N) globally for every K and N.
