  We construct a Hopf algebra on integer binary relations that contains under
the same roof several well-known Hopf algebras related to the permutahedra and
the associahedra: the Malvenuto-Reutenauer algebra on permutations, the
Loday-Ronco algebra on planar binary trees, and the Chapoton algebras on
ordered partitions and on Schr\"oder trees. We also derive from our
construction new Hopf structures on intervals of the weak order on permutations
and of the Tamari order on binary trees.
