1 [similar to S7] done


,
,
,
,

ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s][s][s[s]][s][s]],"MaxSize"200000,"MaxSteps"1000]],PlotRangeAll]

2 done


,
,
,
,

ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s[s][s]]][s][s[s]],"MaxSize"200000,"MaxSteps"1000]],PlotRangeAll]

3 done


,
,
,
,

ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s][s]][s][s[s[s]]],"MaxSize"200000,"MaxSteps"1000]],PlotRangeAll]

4 done


,
,
,
,

ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s][s]][s][s[s][s]],"MaxSize"200000,"MaxSteps"1000]],PlotRangeAll]

5 done


,
,
,
,

ListStepPlot[Differences[LeafCount/@CombinatorFixedPointList[s[s[s[s]][s]][s][s[s]],"MaxSize"200000,"MaxSteps"1000]],PlotRangeAll]

6 done


,
,
,
,

In[]:=
ListStepPlot[Differences[Differences[LeafCount/@CombinatorFixedPointList[s[s][s][s[s[s]]][s[s]],"MaxSize"20000,"MaxSteps"1000]]],PlotRangeAll]
Out[]=

7 done

8 done

9 done

10 done

11 done

12 done

13 done

14 done

15

16 done

17 done

18 done

19 done

20 done

21 done

22 done

23 done

24 done

25 done

26

27

28 transferred

29

30

31 done

32 halting

33 done

34 transferred

35 done

36 halting

37 halting

38 transferred

39 kinda done

40

41

42 done

43 repeatish

44

45

46

Outtakes

There can also be regular [[slightly slower than ]] exponential growth, as in s[s[s]][s][s[s[s]]][s], where the differences basically double in size t/XXXX steps: [[[[???????]]]]]
Sometimes it looks as if there’ll be regular exponential behavior, but it’s not completely clear: