[Right triangle ⏵ may be expanded, down triangle ⏷ to close. Button = tree pop-up. × = close pop-up.]

Terminal: run. Derivation Graphs: (left-to-right) compact / full; (top-down) full / compact.

Variants:
The mechanic who fixed the car packed his tools / The mechanic who carefully fixed the car packed his tools / The mechanic who fixed the car packed his tools carefully
Simpler:
The mechanic fixed the car / The mechanic carefully fixed the car / Carefully, the mechanic fixed the car / The mechanic packed his tools / The mechanic packed his tools carefully / Carefully, the mechanic packed his tools

g [the,mechanic,fixed,the,car,carefully] [the,mechanic,fixed,the,car,carefully] [the,mechanic,carefully,fixed,the,car] [the,mechanic,carefully,fixed,the,car] [the,mechanic,fixed,the,car,carefully]->[the,mechanic,carefully,fixed,the,car] [the,mechanic,carefully,packed,his,tools] [the,mechanic,carefully,packed,his,tools] [the,mechanic,packed,his,tools,carefully] [the,mechanic,packed,his,tools,carefully] [the,mechanic,carefully,packed,his,tools]->[the,mechanic,packed,his,tools,carefully] [the,mechanic,who,fixed,the,car,carefully,packed,his,tools] [the,mechanic,who,fixed,the,car,carefully,packed,his,tools] [the,mechanic,who,carefully,fixed,the,car,packed,his,tools] [the,mechanic,who,carefully,fixed,the,car,packed,his,tools] [the,mechanic,who,fixed,the,car,carefully,packed,his,tools]->[the,mechanic,who,carefully,fixed,the,car,packed,his,tools] [carefully,,,the,mechanic,who,fixed,the,car,packed,his,tools] [carefully,,,the,mechanic,who,fixed,the,car,packed,his,tools] [the,mechanic,fixed,the,car] [the,mechanic,fixed,the,car] [the,mechanic,fixed,the,car]->[the,mechanic,fixed,the,car,carefully] [the,mechanic,carefully,fixed,the,car]->[the,mechanic,fixed,the,car,carefully] [carefully,,,the,mechanic,fixed,the,car] [carefully,,,the,mechanic,fixed,the,car] [the,mechanic,carefully,fixed,the,car]->[carefully,,,the,mechanic,fixed,the,car] [the,mechanic,packed,his,tools] [the,mechanic,packed,his,tools] [the,mechanic,packed,his,tools]->[the,mechanic,carefully,packed,his,tools] [the,mechanic,packed,his,tools,carefully]->[the,mechanic,carefully,packed,his,tools] [carefully,,,the,mechanic,packed,his,tools] [carefully,,,the,mechanic,packed,his,tools] [the,mechanic,packed,his,tools,carefully]->[carefully,,,the,mechanic,packed,his,tools] [the,mechanic,who,fixed,the,car,packed,his,tools] [the,mechanic,who,fixed,the,car,packed,his,tools] [the,mechanic,who,fixed,the,car,packed,his,tools,carefully] [the,mechanic,who,fixed,the,car,packed,his,tools,carefully] [the,mechanic,who,fixed,the,car,packed,his,tools]->[the,mechanic,who,fixed,the,car,packed,his,tools,carefully] [the,mechanic,who,carefully,fixed,the,car,packed,his,tools]->[the,mechanic,who,fixed,the,car,packed,his,tools,carefully] [the,mechanic,who,fixed,the,car,packed,his,tools,carefully]->[the,mechanic,who,fixed,the,car,carefully,packed,his,tools] [the,mechanic,who,fixed,the,car,packed,his,tools,carefully]->[carefully,,,the,mechanic,who,fixed,the,car,packed,his,tools]

To the other core examples:

(Chomsky 2021), p9 excerpt. (Examples (2a-b) discussed here.)
Help: blue = parse inside. Abbr.: WS: Workspace; Initial WS: initial heads for Merge after LEX lookup.
×

Words: the mechanic fixed the car carefully
Initial WS 1: carefullyv carthe fixθ vfix:θ:pst INFLv mechanicthe 
WS 1: {fixθ, carthe} carefullyv vfix:θ:pst INFLv mechanicthe 
WS 2: {vfix:θ:pst, {fixθ, carthe}} carefullyv INFLv mechanicthe 
WS 3: {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}} carefullyv INFLv 
WS 4: {carefullyv, {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}}} INFLv 
WS 5: {INFLv, {carefullyv, {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}}}} 
Final WS: {C, {INFLv, {carefullyv, {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}}}}} 
INT/EXT: {C, {INFLv, {carefullyv, {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}}}}}
EXT: the mechanic carefully 3sg pst fix the car
Spellout: the mechanic carefully fixed the car
Blocked: inconsistent with input!
EXT: the mechanic 3sg pst fix the car carefully
Spellout: the mechanic fixed the car carefully
Parse found: the mechanic 3sg pst fix the car carefully
WS 1: {fixθ, carthe} carefullyv vfix:θ:pst INFLv mechanicthe 
WS 2: {vfix:θ:pst, {fixθ, carthe}} carefullyv INFLv mechanicthe [gray]
WS 3: {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}} carefullyv INFLv [gray]
WS 4: {INFLv, {mechanicthe, {vfix:θ:pst, {fixθ, carthe}}}} carefullyv 
WS 1: {fixθ, mechanicthe} carefullyv carthe vfix:θ:pst INFLv 
WS 2: {vfix:θ:pst, {fixθ, mechanicthe}} carefullyv carthe INFLv 
WS 1: {carthe, mechanicthe} carefullyv fixθ vfix:θ:pst INFLv 
WS 2: {fixθ, {carthe, mechanicthe}} carefullyv vfix:θ:pst INFLv 
WS 3: {vfix:θ:pst, {fixθ, {carthe, mechanicthe}}} carefullyv INFLv