How to divide by zero, pathfinder style

[Aleph Null]

This just happened to me.
(I leave out details unimportant to the overall...situation)
So me and this other dude were duking it out in a 1v1 to test our pathfinder characters. He and I both pre-buff ourselves. I cast spellbane to inhibit antimagic field and other castings of spellbane. He also prebuffs himself with spellbane inhibiting other castings of spellbane. We agree that the castings of spellbane inhibit each other mutually.
Mid fight, he disengages from me, casting antimagic field. This disables his spellbane. I then move into melee range with my own spellbane. I have just performed the pathfinder magic/antimagic equivalent of dividing by zero.
Let me explain. My spellbane inhibits his antimagic field. This causes his spellbane to come back up, and they both inhibit each other. The antimagic field then comes back up, inhibiting his spellbane, causing my spellbane to come back up and inhibit the antimagic field...you get the idea.
Thoughts on how this should resolve?

[Eldonauran]

Sure. As a GM, I suggest making opposed caster level checks. The spells are effectively attempting to suppress each other simultaneously. Highest caster level check wins, similar to a dispel magic attempt. If neither player is satisfied, that's ok, we'll see who survives the resulting explosion of magical energies as the spells overload each other. Simulatenous 20d6 untyped damage explosions, centered on each of you, roll reflex?

[InvisibleBison]

My spellbane inhibits his antimagic field. This causes his spellbane to come back up, and they both inhibit each other. The antimagic field then comes back up, inhibiting his spellbane, causing my spellbane to come back up and inhibit the antimagic field

Wouldn't the antimagic field coming back up suppress both spellbanes?

[Xenopax]

Wouldn't the antimagic field coming back up suppress both spellbanes?

But My AMF would be renegated by the Spell Bane. Since Spell bane isn't suppressed By an AMF then it would just end up as looping. This other guy told us that there was actually PF canon for this that ended up in a Dead Magic zone for a Mile.

[Crow_Nightfeath]

Well the two spellbanes are cancelling each other out, the antimagic field has no spell cancelling it anymore. yours can't just retrigger just cause a spell that it's cast against pops up, it is being cancelled by the other spell bane.

Edit: oh.. wait I forgot that the antimagic field was inhibiting his spellbane.. as a DM I would still rule just to keep it moving that the antimagic field is the one active currently.. I swear with this sort of stuff people are purposely trying to force problems, and drag things out.

[Xenopax]

I swear with this sort of stuff people are purposely trying to force problems, and drag things out.

Well the reason was because I wanted to even the Playing field. They had suppressed all Arcane Magic that was close to them so all I could do was shoot them with my rifle. This way neither of us had magic to rely on.

[Florian]

Using the regular combat rules, so initiative based, the Spellbanes don't cancel each other out. The first one moving his Spellbane onto the other Spellbane will suppress that and keep his own up and running.

[Xenopax]

The spell bane is suppressed already. It just reactivates after they suppress the AMF

[Eldest]

Further complicating the matter (I was sorta the gm for this? it was a random duel between PCs for another game) is that Source Severance (https://www.d20pfsrd.com/magic/all-spells/s/source-severance/) was in effect, tuned to arcane, on Aleph's character.

[Psyren]

I would just rule that AMF can't stop Spellbane at all (whether AMF is specified or not.) That's how I read it anyway.