Depending on his interpretation of the rules about trapped instructions, one could just build a loop in the x86 page tables. Those are usually a tree linked by pointers, and any page table lookup can create another page fault that creates another lookup that...

Leads to x86 page table MMU magic being turing complete: https://github.com/jbangert/trapcc

And the simplest thing you can do on such a system is just to loop indefinitely, thus creating a simple instruction with a memory access (mov or anything, doesn't really matter, even the instruction fetch for a nop would work) to take infinite time.