  We prove the NP-completeness of the integer multiflow problem in planar
graphs, with the following restrictions: there are only two demand edges, both
lying on the infinite face of the routing graph. This was one of the open
challenges concerning disjoint paths, explicitly asked by M\"uller. It also
strengthens Schw\"arzler's recent proof of one of the open problems of
Schrijver's book, about the complexity of the edge-disjoint paths problem with
terminals on the outer boundary of a planar graph. We also give a directed
acyclic reduction. This proves that the arc-disjoint paths problem is
NP-complete in directed acyclic graphs, even with only two demand arcs.
