Pensieve header: km at $k=1 with up to 15 inputs.

SetDirectory["C:\\drorbn\\AcademicPensieve\\Projects\\SL2Portfolio2"];
<< KnotTheory`;
<<"../Profile/Profile.m";
(*<<"Archive/Engine-Speedy-190317.m";*) (*174.874 Seconds *)
<<"Engine-Speedy.m"; (*169.953 Seconds*)
<<"Objects.m";
BeginProfile[];

$k=1;  Clear[km];

km[1]=(Subscript[𝔼, {1}->{1}])[(Subscript[a, 1]) (Subscript[α, 1])+t (Subscript[τ, 1]), (Subscript[x, 1])(Subscript[ξ, 1])+(Subscript[y, 1])(Subscript[η, 1]),1];
km[n_Integer]/;n>1 := km[n] = km[n-1]//(Subscript[km, 1,n->1])

km[4]

Table[LeafCount /@ List@@km[n], {n,15}] // MatrixForm

ListLogLogPlot[Table[LeafCount[km[n][[3]]], {n,15}]]

N@Table[((Log@LeafCount[km[n][[3]]])/(Log[n])), {n,2,15}]

PrintProfile[]