Fantastic effort to combine grammar and discourse, to analyse genre and field. Critical focus is on lexical, conjunction and reference items, for which answer 1 is great text to analyse. You could go a little further and simplify. Here with lexical items in yellow and conjunction, reference, appraisal items in blue.
S1. A system call is a request made by a process to the operating system in order to perform tasks only the operating system can complete.
Retrieving a file from a disk, or retrieving/displaying inputs/outputs, are examples of this
nuclear relations, activity sequence and conjunction - what’s going on
line 1 defines system call as type of request from process to operating system
line 2 explains what operating system does then (in order to, only)
line 3 exemplifies types of tasks requested by system call (examples of this)
(nuclear relations are lexical relations within clauses, configured by grammar)
taxonomic relations - why it makes sense
line 1 system call is a type of call, call and request are synonyms, process is technical part of computing field,
lines 1-2 operating and perform tasks are synonymous, operating system is repeated, complete is part of task
lines 2-3 retrieving/displaying are types of task, file/disk/inputs/outputs are parts of operating system
 The "fantastic effort" that Rose applauds misconstrues these two clauses of a student's exam answer as attributive rather than identifying. See clause analysis here.
As the clause analysis shows — but which Rose's discourse semantic analysis doesn't — in the first clause, the student decodes a system call and, in the second clause, the student then encodes examples of this.
 To be clear, in Martin's discourse semantics:
- 'nuclear relations' are expansion relations — mostly misapplied — between experiential elements of clause and group structure;
- 'activity sequence' is misconstrued as an aspect of field, not discourse semantics;
- 'conjunction' is the logical system of discourse semantics — which confuses structural (logical) deployments of expansion with cohesive (textual) deployments;
- 'what's going on' could be either field ('activity sequence') or genre ('social process').
 This is only part of the definition, as the grammatical analysis makes clear. Rose's analysis makes no use of any of the discourse semantic resources: nuclear relations, activity sequence or conjunction.
 This part of the definition construes purpose, not time. Here Rose has applied the discourse semantic resource of conjunction to an embedded clause complex, but misidentified the expansion relation.
 As the clause analysis shows, this clause encodes examples of a system call. In the absence of a clause analysis, Rose misconstrues the meaning realised by the clause, as evinced by his "tasks requested by a system call"; cf. 'a system call is a request made by a process…'. Again, Rose's analysis makes no use of any of the discourse semantic resources: nuclear relations, activity sequence or conjunction.
 Martin's nuclear relations (1992: 309-21) are not lexical relations, but (misapplied) expansion relations between elements of the experiential function structure of clauses (Process, Medium, Range, circumstance), nominal groups (Thing, Classifier, Epithet, Qualifier) and verbal groups (Event, Particle, Quality). Rose has used none of these relations in his analysis.
 As demonstrated here, Martin's experiential discourse semantic system, termed ideation, is a confusion of lexical cohesion (textual metafunction), lexis as most delicate grammar and expansion relations between elements of function structures (logical metafuction). The taxonomic relations Rose refers to here is the 'lexical cohesion' component. That is, these relations help to make the text cohesive.
 This is not a taxonomic relation in the text — despite the use of 'part' to suggest meronymy.
 The suggestion here is that there is a meronymic relation between 'complete' (part) and 'task' (whole). This can be examined through the lens of expansion relations. If 'complete' is regarded as a phase of a process, then the type of expansion is elaboration (Halliday & Matthiessen 2014: 569ff), whereas a meronymic relation is one of extension (Halliday & Matthiessen 1999: 89). Halliday & Matthiessen (1999: 91) provide a different argument:
We can certainly recognise that processes have phases — 'begin to do, keep doing, stop doing'; but it is not immediately clear that these form a process meronymy analogous to the parts of a participant. Although we might reconstrue he began to dance metaphorically as the beginning of his dance on the model of 'the beginning of the book', this is a metaphorical reification of the process 'dance' and we have to be cautious in interpreting the implications for the congruent process 'dance'. If we probe a little further, we can see that process phase is concerned with the occurrence of a process in time — its temporal unfolding: 'begin to do' means 'begin to be actualised (to occur) as doing in time'. In contrast, participant meronymy is not tied to the existence of a participant in referential space.
Despite claiming to provide a discourse semantic analysis of these clauses, Rose makes no use of the system of nuclear relations (discourse semantic ideation) or activity sequences (Martin's register: field), and the one use he makes of discourse semantic conjunction, he gets wrong. Further, in his use of Martin's lexical relations (discourse semantic ideation) — a relabelling of Halliday's lexical cohesion — he misrepresents meronymic relations. Moreover, there was no analysis of appraisal, genre or field.
Most importantly, the fact that the student provided two identifying clauses, with the first decoding a technical term, and the second encoding examples, was not recognised.
Given all of the above, it is fair to say that the aim of the exercise was not pedagogy.