On the other hand, rather than just making it up like Cobalt, we can go to the regulations.
Originally Posted by LASORS 2010
Complex type An aeroplane certificated for the carriage of at least four persons, having a variable pitch
propeller and retractable landing gear
(Section A, Appendix A, page 34)
(LASORS elsewhere differentiates between "complex SEP" and "complex MEP" - although I can't think of many, if any, non-complex MEP.)
You can of-course only teach on complex types, if you are rated on them themselves. But anybody with a JAR CPL is by definition, because they had to do part of the CPL and pass the skill test on a complex type. If you are a PPL/CRI without complex, then you can't teach on complex.
"Non-high performance" is anything not listed by EASA as "HPA" or "High Performance Aeroplane". If you look at the list
here; if a type has "HPA" next to it, then it's High Performance. If the type isn't listed, or doesn't have HPA next to it, then it isn't.
Fiddly, but the information is all there if you know where to look for it. And don't just make it up!
G