To take someone to task for not referring to the regulations and then to refer to LASORS is, to say the least, something of an own goal. LASORS is most emphatically not a regulatory document and has nothing whatever to say about EU regulation (as opposed to current JAA Requirements), which was the subject of the original question.
The thing to remember when dealing with EU regulation is that you cannot consider one element (e.g. Part-FCL) in isolation but have to consider the whole regulatory structure - in the case of aircrew licensing, for example, you need to consult the Basic Regulation (Regulation (EC) 218/2008), the Aircrew Regulation (Regulation (EU) 1178/2011) and its annexes (Part-FCL, etc.) and the associated AMCs and GM in order to get the full picture.
The definition of a complex motor powered aircraft is in Article 3 of the Basic Regulation and cobalt was pretty close in his paraphrasing. The use of the term 'complex' in relation to the aircraft used in the CPL(A) course is incorrect - neither JAR-FCL1 nor Part-FCL uses the term in this context, both referring, in full, to "an aeroplane certificated for the carriage of at least four persons [with] a variable pitch propeller and retractable landing gear". It could be said that the 'unfortunate' thing is not that EASA chose to properly define the word 'complex' but that pilots had previously chosen to use the term incorrectly.
A high performance aircraft is one that is so defined in the EASA class and type rating list. Consequently, a CRI/CRE may exercise his privileges on any type that is not defined as either HPA or a complex motor powered aircraft.
The requirements for a TRI(SPA) certificate are to be found in Part-FCL at FCL.915.TRI