In[]:=

<<CombinatorEvolve`

In[]:=

ParallelEvaluate[<<CombinatorEvolve`]

Out[]=

{Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null,Null}

In[]:=

CombinatorSignature[cbr_,n_,tmax_]:=CombinatorLeftmostOutermostLeafCounts[cbr,#,tmax]&/@Groupings[Table[e,n],Construct2]

In[]:=

#(ListLinePlot[#,PlotTheme"Minimal",ImageSize30]&/@Union[If[Length[Union[#]]<5,Nothing,#]&/@Differences/@CombinatorSignature[#,4,50]])&/@({e[x_][y_]#}&)/@Union[Flatten[Groupings[#,Construct2]&/@Tuples[{x,y},4]]]

Out[]=

In[]:=

DeleteCases[#(ListStepPlot[#,PlotTheme"Minimal",ImageSize30,PlotRangeAll]&/@Union[If[Length[Union[#]]<5,Nothing,#]&/@Differences/@CombinatorSignature[#,4,200]])&/@({e[x_][y_]#}&)/@Union[Flatten[Groupings[#,Construct2]&/@Tuples[{x,y},4]]],_{}]

Out[]=

{e[x_][y_]x[x[y[x]]]}{

},{e[x_][y_]x[x[y[y]]]}{

},{e[x_][y_]x[y[x[x]]]}{

},{e[x_][y_]x[y[x[y]]]}

,{e[x_][y_]x[y[y[x]]]}{

},{e[x_][y_]x[y[y[y]]]}{

},{e[x_][y_]x[x[y][y]]}{

},{e[x_][y_]x[y[x][x]]}{

},{e[x_][y_]x[y[x][y]]}{

},{e[x_][y_]x[y[y][x]]}{

},{e[x_][y_]x[y[y][y]]}{

},{e[x_][y_]y[x[x[y]]]}{

},{e[x_][y_]y[x[y[x]]]}{

},{e[x_][y_]y[x[y[y]]]}{

},{e[x_][y_]y[y[x[x]]]}{

},{e[x_][y_]y[y[x[y]]]}{

},{e[x_][y_]y[y[y[x]]]}{

},{e[x_][y_]y[x[y][x]]}{

},{e[x_][y_]y[y[x][x]]}{

},{e[x_][y_]y[y[x][y]]}{

},{e[x_][y_]x[x][y[y]]}{

},{e[x_][y_]x[y][x[y]]}{

},{e[x_][y_]x[y][y[x]]}{

},{e[x_][y_]x[x[y]][x]}{

},{e[x_][y_]x[x[y]][y]}{

},{e[x_][y_]x[y[x]][y]}{

},{e[x_][y_]y[x[x]][y]}{

},{e[x_][y_]y[x[y]][x]}{

},{e[x_][y_]y[x[y]][y]}{

},{e[x_][y_]y[y[x]][x]}{

}

In[]:=

DeleteCases[#(ListLinePlot[#,PlotTheme"Minimal",ImageSize30,PlotRangeAll]&/@Union[If[Length[Union[#]]<5,Nothing,#]&/@Differences/@CombinatorSignature[#,4,200]])&/@({e[x_][y_]#}&)/@Union[Flatten[Groupings[#,Construct2]&/@Tuples[{x,y},4]]],_{}]

Out[]=

{{e[x_][y_]x[x[y[x]]]}{

},{e[x_][y_]x[x[y[y]]]}{

},{e[x_][y_]x[y[x[x]]]}{

},{e[x_][y_]x[y[x[y]]]}{

},{e[x_][y_]x[y[y[x]]]}{

},{e[x_][y_]x[y[y[y]]]}{

},{e[x_][y_]x[x[y][y]]}{

},{e[x_][y_]x[y[x][x]]}{

},{e[x_][y_]x[y[x][y]]}{

},{e[x_][y_]x[y[y][x]]}{

},{e[x_][y_]x[y[y][y]]}{

},{e[x_][y_]y[x[x[y]]]}{

},{e[x_][y_]y[x[y[x]]]}{

},{e[x_][y_]y[x[y[y]]]}{

},{e[x_][y_]y[y[x[x]]]}{

},{e[x_][y_]y[y[x[y]]]}{

},{e[x_][y_]y[y[y[x]]]}{

},{e[x_][y_]y[x[y][x]]}{

},{e[x_][y_]y[y[x][x]]}{

},{e[x_][y_]y[y[x][y]]}{

},{e[x_][y_]x[x][y[y]]}{

},{e[x_][y_]x[y][x[y]]}{

},{e[x_][y_]x[y][y[x]]}{

},{e[x_][y_]x[x[y]][x]}{

},{e[x_][y_]x[x[y]][y]}{

},{e[x_][y_]x[y[x]][y]}{

},{e[x_][y_]y[x[x]][y]}{

},{e[x_][y_]y[x[y]][x]}{

},{e[x_][y_]y[x[y]][y]}{

},{e[x_][y_]y[y[x]][x]}{

}}

In[]:=

DeleteCases[#(ListLinePlot[#,PlotTheme"Minimal",ImageSize30,PlotRangeAll]&/@Union[If[Length[Union[#]]<5,Nothing,#]&/@Differences/@CombinatorSignature[#,5,200]])&/@({e[x_][y_]#}&)/@Union[Flatten[Groupings[#,Construct2]&/@Tuples[{x,y},4]]],_{}]

Out[]=