In[]:=
ResourceFunction["MultiwayCombinator"]
Out[]=
In[]:=
ResourceFunction["MultiwayCombinator"][{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x}"Sequential",s[s[s[s][s]]][s][s][k],12,"StatesGraphStructure"]
Out[]=
In[]:=
ResourceFunction["MultiwayCombinator"][{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x}(First[#]&),s[s[s[s][s]]][s][s][k],2,"StatesGraph"]
In[]:=
ResourceFunction["MultiwayCombinator"][{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x}"Sequential",s[s][s][s[s]][s][s],40,"StatesGraphStructure"]
Out[]=
In[]:=
ToExpression/@VertexList[%];
In[]:=
LeafCount/@%
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,68,77,87,97,107,117,127,137,148,159,170,193,216,239,262,286,310,346,407,468,529,590,652,714,776,850,987,1124}
In[]:=
ListLinePlot[%311]
Out[]=
In[]:=
LeafCount/@SKFixedPointEvolveList[s[s][s][s[s]][s][s],1000]
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,87,115,149,187,215,243,272,301,389,417,426,441,450,459,468,483,492,501,529,558,587,675,684,699,708,717,726,741,750,759,768,777,792,817,842,851,860,875,900,925,934,943,958,983}
In[]:=
Position[%314,87]
Out[]=
{{14}}
In[]:=
SKFixedPointEvolveList[s[s][s][s[s]][s][s],1000][[14]]
Out[]=
s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s]][s[s[s[s]][s]][s]][s[s[s]][s[s[s[s]][s]][s]][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]][s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s]][s[s[s[s]][s]][s]][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]]]
In[]:=
%310[[14]]
Out[]=
s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s[s]][s[s[s[s]][s]][s]]]][s[s][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s]][s][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s[s]][s[s[s[s]][s]][s]]]]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]
In[]:=
SKFixedPointEvolveList[s[s][s][s[s]][s][s],1000][[13]]
Out[]=
s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s]][s[s[s[s]][s]][s]][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]]
In[]:=
%310[[13]]
Out[]=
s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s[s]][s[s[s[s]][s]][s]]]][s[s][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s]][s][s[s[s[s]][s[s[s[s]][s]][s]]]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]
In[]:=
%===%%
Out[]=
False
In[]:=
SameQ@@@Transpose[{Take[%310,14],Take[SKFixedPointEvolveList[s[s][s][s[s]][s][s],1000],14]}]
Out[]=
{True,True,True,True,True,True,True,True,True,True,True,True,False,False}
In[]:=
e12=SKFixedPointEvolveList[s[s][s][s[s]][s][s],1000][[12]]
Out[]=
s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s]][s[s[s[s]][s]][s]][s[s[s[s]][s[s[s[s]][s]][s]]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]
In[]:=
ResourceFunction["MultiwayCombinator"][{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x},s[s][s][s[s]][s][s],15,"StatesGraphStructure"]
Out[]=
In[]:=
Position[e12,s[_][_][_]|k[_][_]]
Out[]=
{{1,0,1},{1}}
In[]:=
SKStepLargest[expr_]:=MapAt[Replace[{s[x_][y_][z_]x[z][y[z]],k[x_][y_]x}],expr,{First[ReverseSortBy[Position[expr,s[_][_][_]|k[_][_]],Length],{}]}]
In[]:=
SKFixedPointEvolveListLargest[expr_,max_Integer]:=Most[NestWhileList[SKStepLargest,expr,#1=!=#2&&LeafCount[#2]<max&,2]]
In[]:=
LeafCount/@SKFixedPointEvolveListLargest[s[s][s][s[s]][s][s],1000]
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,68,77,87,97,107,117,127,137,148,159,170,193,216,239,262,286,310,346,407,468,554,640,726,837,948}
In[]:=
LeafCount/@%310
Out[]=
{7,8,8,11,11,11,12,17,25,33,41,50,59,68,77,87,97,107,117,127,137,148,159,170,193,216,239,262,286,310,346,407,468,529,590,652,714,776,850,987,1124}
In[]:=
Position[%,529]
Out[]=
{{34}}
In[]:=
Position[SKFixedPointEvolveListLargest[s[s][s][s[s]][s][s],1000][[33]],s[_][_][_]|k[_][_]]
Out[]=
{{1,0,1,1,1,0,1,1,0,1,0,1,0},{1,0,1,1,1,0,1,1,0,1,0,1,1},{1,0,1,1,1,0,1,1,0,1},{1,0,1,1,1,0,1,1,0},{1,0,1,1,1,0,1},{1,0,1,1,1,0},{1,0,1,1},{1,0,1},{1}}
In[]:=
Length/@%
Out[]=
{13,13,10,9,7,6,4,3,1}
In[]:=
FunctionToApplication[s[s[s[s]][s[s[s[s]][s]][s]]][s[s[s[s[s]][s[s[s[s]][s]][s]]]][s[s][s[s[s[s]][s[s[s[s]][s]][s]]]][s[s[s[s]][s]][s][s[s[s[s]][s[s[s[s]][s]][s]]]]]][s[s[s[s]][s[s[s[s]][s]][s]]]]]]
Out[]=
s(s(ss)(s(s(ss)s)s))(s(s(s(ss)(s(s(ss)s)s)))(ss(s(s(ss)(s(s(ss)s)s)))(s(s(ss)s)s(s(s(ss)(s(s(ss)s)s)))))(s(s(ss)(s(s(ss)s)s))))
In[]:=
ExpressionGraph[%]
Out[]=
In[]:=
TreePlot[%]
/. is neither lexicographic, nor does it burrow into already inhabited burrows
/. is neither lexicographic, nor does it burrow into already inhabited burrows