A question about Interior Multiplication in 𝕆

Before executing what follows, one needs to load packages “FreeLie.m’’, “AwCalculus.m’’, “FAA.m’’, “EmergentChordDiagrams.m’’

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

Let us consider the following two elements:

T1=(Subscript[𝕆, AR,{x},{1}])[(Subscript[𝒜, 0])[(Subscript[AW, 1])[x]+(Subscript[AW, 1])[x,x]]]
T2=(Subscript[𝕆, AR,{x},{1}])[(Subscript[𝒜, 0])[(Subscript[AW, 1])[]+(Subscript[AW, 1])[x]+(Subscript[AW, 1])[x,x]]]

(Subscript[IM, 2])[T1,T1]
(Subscript[IM, 2])[T2,T2]
(Subscript[IM, 2])[T1,T2]

The first output, (Subscript[IM, 2])[T1,T1], should not have the degree 3 part, but it does...  It seems that (Subscript[IM, d]) does not return the correct answer when both the inputs have the trivial constant term. Why does it happen?  Furthermore, if we take powers of such an element,then a bug appears:

(Subscript[IM, 2])[T1,T1,T1]
(Subscript[IM, 2])[T1,T1,T1,T1]

It seems that the problem comes from applying the strand multiplication to the zero element in 𝕆...

(Subscript[𝕆, AR,{x},{1,2}])[(Subscript[𝒜, 0])[(Subscript[AW, 1])[](Subscript[AW, 2])[]]]
(Subscript[𝕆, AR,{x},{1,2}])[(Subscript[𝒜, 0])[(Subscript[AW, 1])[](Subscript[AW, 2])[]]]//(Subscript[sm, 1,2->3])
(Subscript[𝕆, AR,{x},{1,2}])[(Subscript[𝒜, 0])[0 (Subscript[AW, 1])[](Subscript[AW, 2])[]]]
(Subscript[𝕆, AR,{x},{1,2}])[(Subscript[𝒜, 0])[0 (Subscript[AW, 1])[](Subscript[AW, 2])[]]]//(Subscript[sm, 1,2->3])