A DESCRIPTION OF THE PROBLEM :
The section "Operations on URI instances" states:

 Relativization, finally, is the inverse of resolution: For any two normalized URIs u and v,

    u.relativize(u.resolve(v)).equals(v) and
    u.resolve(u.relativize(v)).equals(v) .

This is not true for at least the following two cases:

1. Base URI (u) that doesn't end with an empty segment:

    URI u = new URI("http://a.ch/a")
    URI v = new URI("http://a.ch/a/b")
    u.resolve(u.relativize(v))
    // "http://a.ch/b" != "http://a.ch/a/b"
    u.relativize(u.resolve(v))
   // "b" != "http://a.ch/a/b"

2. Target URI (v) that contains top-level ".." segments:

    URI u = new URI("http://a.ch/a")
    URI v = new URI("../b")
    u.resolve(u.relativize(v))
    // "http://a.ch/../b" != "../b"
    u.relativize(u.resolve(v))
    // "http://a.ch/../b" != "../b"

EXPECTED VERSUS ACTUAL BEHAVIOR :
EXPECTED -
1. No invariant about relativization and resolution
2. Proper documentation about relativization
  - how it handles non-empty segments at end of base path
  - that relativization will never introduce ".." segments
ACTUAL -
Relativization, finally, is the inverse of resolution: For any two normalized URIs u and v,

    u.relativize(u.resolve(v)).equals(v) and
    u.resolve(u.relativize(v)).equals(v) .


URL OF FAULTY DOCUMENTATION :
http://docs.oracle.com/javase/7/docs/api/java/net/URI.html