<<MultiwaySystems/Multiway.m
mrule1={{"ABA""ABBAB","AB""","ABABBB""AAAAABA"},"ABABAB"};
XMWUEvolveTotals[First[mrule1],{Last[mrule1]},200]
{1,3,6,8,6,3,2,3,2,3,4,5,5,5,4,2,3,4,5,4,4,3,3,3,2,4,3,4,3,3,3,4,5,3,4,3,3,3,4,5,5,5,3,3,3,4,5,5,5,5,4,3,4,5,5,5,5,4,5,5,5,5,5,5,4,5,5,7,6,5,5,4,5,5,7,6,7,6,4,5,5,7,6,7,6,6,6,5,7,6,7,6,6,6,7,8,6,7,6,6,6,7,8,8,8,6,6,6,7,8,8,8,8,7,6,7,8,8,8,8,7,8,8,8,8,8,8,7,8,8,10,9,8,8,7,8,8,10,9,10,9,7,8,8,10,9,10,9,9,9,8,10,9,10,9,9,9,10,11,9,10,9,9,9,10,11,11,11,9,9,9,10,11,11,11,11,10,9,10,11,11,11,11,10,11,11,11,11,11,11,10,11,11,13,12,11,11,10,11,11,13}
Differences[XMWUEvolveTotals[First[mrule1],{Last[mrule1]},1000]];
ListPlot[%,PlotJoinedTrue];
XMWEvolveTotals[First[mrule1],{Last[mrule1]},200]
{1,3,6,8,6,3,2,3,2,3,4,5,5,5,4,2,3,4,5,5,6,6,5,4,4,5,5,6,6,6,6,7,6,5,6,6,6,7,8,8,8,7,6,6,7,8,9,9,9,9,7,7,8,9,10,10,10,9,10,9,9,10,10,11,10,11,11,12,11,10,11,11,12,12,13,13,13,12,11,12,13,14,14,14,14,14,13,13,15,15,15,15,15,15,16,16,15,16,16,16,16,17,18,18,17,17,17,17,18,19,19,19,20,18,18,19,20,20,20,21,20,21,21,21,21,21,22,21,22,23,24,23,22,23,22,23,24,25,25,26,25,23,24,25,26,26,27,27,27,26,26,27,27,28,28,28,29,30,29,28,29,29,29,30,31,32,32,31,30,30,31,32,33,34,34,34,32,32,33,34,35,35,36,35,36,35,35,36,36,37,37,38,38,39,38,37,38,38,39,40,41}
Differences[MWCharGrowth[mrule1,200]]
{2,3,2,-2,-3,-1,1,-1,1,1,1,0,0,-1,-2,1,1,1,0,1,0,-1,-1,0,1,0,1,0,0,0,1,-1,-1,1,0,0,1,1,0,0,-1,-1,0,1,1,1,0,0,0,-2,0,1,1,1,0,0,-1,1,-1,0,1,0,1,-1,1,0,1,-1,-1,1,0,1,0,1,0,0,-1,-1,1,1,1,0,0,0,0,-1,0,2,0,0,0,0,0,1,0,-1,1,0,0,0,1,1,0,-1,0,0,0,1,1,0,0,1,-2,0,1,1,0,0,1,-1,1,0,0,0,0,1,-1,1,1,1,-1,-1,1,-1,1,1,1,0,1,-1,-2,1,1,1,0,1,0,0,-1,0,1,0,1,0,0,1,1,-1,-1,1,0,0,1,1,1,0,-1,-1,0,1,1,1,1,0,0,-2,0,1,1,1,0,1,-1,1,-1,0,1,0,1,0,1,0,1,-1,-1,1,0,1,1,1}
XMWUEvolveTotals[{"A""AA"},{"A"},20]
{1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
XMWUEvolveTotals[{"A""AA","A""B"},{"A"},20]
$Aborted
XMWUEvolveTotals[{"A""AA","A""B"},{"A"},4]
{1,2,3,5,8}
XMWUEvolveTotals[{"A""AA","A""B"},{"A"},4]
{1,2,3,5,8}
MWBigGraphic[rr_,init_,t_,rs_:0.2]:=RHInset[Surround[MWGraphic[MWEvolveListT[rr,init,t]]],MWCharRuleGraphic[rr],{rs,.04}]
Show[MWBigGraphic[{"A""AA","A""B"},{"A"},5]];
Show[MWBigGraphic[{"A""AB","B""A"},{"A"},5]];
XMWEvolveTotals[{"A""AA","A""B"},{"A"},10]
{1,2,3,5,8,13,21,34,55,89,144}
XMWEvolveTotals[ToChars[{{0,0,1,1}{0},{0,0,0}{1,0,0},{1,0,0,1,1}{1,1,0,0},{1,1,0}{0,1,1,1}}],{ToChars[{1,0,0,1,1,1,0}]},1000];
ListPlot[Differences[%],PlotJoinedTrue];
ListPlot[%,PlotJoinedTrue];
ListPlot[Differences[%12],PlotJoinedTrue];
XMWUEvolveTotals[ToChars[{{0,0,1,1}{0},{0,0,0}{1,0,0},{1,0,0,1,1}{1,1,0,0},{1,1,0}{0,1,1,1}}],{ToChars[{1,0,0,1,1,1,0}]},1000];
ListPlot[%,PlotJoinedTrue];
The following rules are complete & consistent:
Simplest types of cases: length of proof is logarithm of length of string.... (this happens if the rule just adds a single symbol to every theorem)
Maximum proof length for theorems of length 8: 14 steps [probably].