Pensieve header: (123) = [(412),(253)] = [[(341),(152)],[(125),(543)]] = ...

Decommute = p[j_,k_,m_] :>  Module[{i,l},
{i,l}=Complement[Range[5],{j,k,m}];
c[p[i,j,k],p[k,l,m]]
];
Format[p[i_,j_,k_]] := "("<>ToString[i]<>ToString[j]<>ToString[k]<>")";
Format[c[a_,b_]] := "["<>ToString[a]<>","<>ToString[b]<>"]";

p[2,3,5] /. Decommute

p[1,2,3] /. Decommute

p[1,2,3] /. Decommute /. Decommute

p[1,2,3] /. Decommute /. Decommute /. Decommute

p[1,2,3] /. Decommute /. Decommute /. Decommute /. Decommute