Initialization

SetDirectory["/home/drorbn/AcademicPensieve/People/Ens/171205"];
<< FreeLie.m;
$SeriesShowDegree=1;
$IterationLimit = (2^20);
Arb=Arbitrator -> (Replace[#, _:>RandomInteger[{-100,100}], 1]&);

Testing The Reidemeister III Syzygy

FF=DKS[4,FFs];
R3Info=SeriesSolve[FF,(FF^(σ[1,3,4,5]))+(FF^(σ[13,2,4,5]))-(FF^(σ[1,2,4,5]))-(FF^(σ[12,3,4,5]))≡DKS[0],Arb];

Do[FF@{k}; Print[Length[Last[#]] & /@ Read[R3Info]], {k,12}]

ArbR3 = Length[Last[#]] & /@ Read[R3Info]