[twic]

If the two hostnames resolve to the same IP address, they are equivalent. This could happen if initech.com was a default domain. This is a very standard situation in internal networks which i am surprised you are not familiar with.

[franga2000]

I am quite familiar with that kind of setup and it's even further from equivalent than what I assumed you were referring to. Shared web hosting is the common example, but some other protocols are capable of distinguishing between hostnames.

google.com and maps.google.com resolve to the same address but are not equivalent. Even if your example and many others are equivalent, there are many that aren't. A general library should not make assumptions like that, unless they hold 100% of the time.

[twic]

You asked for a single example of two 'equal' URLs whose strings don't match up, and now you've got one.

[franga2000]

Looking back, I did phrase it ambiguously. What I meant was two URLs that are equal by definition, (no matter the server config, assuming standards compliance). A (general) library should make no more assumptions than the standard it implements. What I was asking about were cases, similar to http://h/p?x1=a&x2=b being equal to http://h/p?x2=b&x1=a since query parameter order is defined to not matter.

The spec I am mostly familiar with is, however, rather new, and whatever standard controlled URLs at the time (if any) might have made more assumptions.