In[]:=
LeafCount/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,87,115,149,187,215,243,272,301}
In[]:=
Depth[#,HeadsTrue]&/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=
{6,6,6,7,7,7,7,8,9,10,11,12,12,13,14,15,15,15,16,17,17}
In[]:=
ToDAG[expr_]:=Graph[Catenate[Function[e,MapIndexed[DirectedEdge[e,#,First[#2]-1]&,Level[e,{1},HeadsTrue]]]/@Union[Level[expr,{0,Infinity},HeadsTrue]]],EdgeStyle{DirectedEdge[_,_,0]Directive[Darker[Red],Thick],DirectedEdge[_,_,1]Pink,DirectedEdge[_,_,"Evolution"]Directive[Red,Dotted]}]
Union[
ByteCount[
In[]:=
ByteCount/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=
{288,336,336,480,480,480,528,768,1152,1536,1920,2352,2784,4128,5472,7104,8928,10272,11616,13008,14400}
In[]:=
ByteCount[#]/LeafCount[#]&/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=

288
7
,42,42,
480
11
,
480
11
,
480
11
,44,
768
17
,
1152
25
,
512
11
,
1920
41
,
1176
25
,
2784
59
,
1376
29
,
5472
115
,
7104
149
,
8928
187
,
10272
215
,
3872
81
,
813
17
,
14400
301

In[]:=
N[%]
Out[]=
{41.1429,42.,42.,43.6364,43.6364,43.6364,44.,45.1765,46.08,46.5455,46.8293,47.04,47.1864,47.4483,47.5826,47.6779,47.7433,47.7767,47.8025,47.8235,47.8405}
In[]:=
ListLinePlot[%]
Out[]=
5
10
15
20
41
42
43
44
45
46
47
48
In[]:=
VertexCount[CombinatorTree[#]]&/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=
{13,15,15,21,21,21,23,33,49,65,81,99,117,173,229,297,373,429,485,543,601}
In[]:=
LeafCount/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,87,115,149,187,215,243,272,301}
In[]:=
2%-1
Out[]=
{13,15,15,21,21,21,23,33,49,65,81,99,117,173,229,297,373,429,485,543,601}
In[]:=
ToDAG/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,

Out[]=
In[]:=
TransitiveReductionGraph[ToDAG[#]]&/@CombinatorEvolveList[s[s][s][s[s]][s][s],20]
Out[]=

,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,
,


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