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In[]:=
ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s][s]]][s][s][s],40000]]
Out[]=

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s[s][s]]]][s][s],2000]]

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s]][s][s][s][s][s],2000]]

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s]][s][s][s][s]],2000]]

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s]][s][s]][s][s],2000]]

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s]][s]][s][s][s],2000]]

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ListLinePlot[LeafCount/@SKFixedPointEvolveList[s[s[s[s[s]][s]]][s][s],2000]]

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