Pensieve header: Solving for V alone (with Kuno). Continues pensieve://Projects/WKO4.

SetDirectory["C:\\drorbn\\AcademicPensieve\\People\\Kuno"];
<< FreeLie.m;

x=LW@"x";y=LW@"y";
bch=BCH[x,y]

bch@5

bch@5//ι

τ=FreeLie`Private`τ;

τ[x,bch]@{6}

{A=LS[{x,y}, As], B=LS[{x,y}, Bs]};
As[x]= 1/2; Bs[y]=0;
msgs=SeriesSolve[{A,B},(ℏ^(-1))(b[LW@x, A]+b[LW@y,B] ≡ LS[0])];
Timing[A@10;]
Length[Last[#]]& /@ Read[msgs]

Timing[A@15;]
Length[Last[#]]& /@ Read[msgs]

Timing[A@16;]
Length[Last[#]]& /@ Read[msgs]

Timing[A@17;]
Length[Last[#]]& /@ Read[msgs]

Timing[A@18;]
Length[Last[#]]& /@ Read[msgs]

tab=Table[Length@AllLyndonWords[k,{x,y}],{k,18}]

2tab-RotateLeft[tab]

Timing[A@19;]
Length[Last[#]]& /@ Read[msgs]