Single Rules + Single Arities on Each Side {{n1,a1}}{{n2,a2}}
Single Rules + Single Arities on Each Side {{n1,a1}}{{n2,a2}}
Arity assumed the same on both sides; n2 > n1 for growth
allsigs=Flatten[Table[{{n1,a}}{{n2,a}},{n1,3},{n2,n1+1,6},{a,3}]]
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Maximum number of symbols:
(Times@@First[#1]+Times@@First[#2])&@@@allsigs
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{3,6,9,4,8,12,5,10,15,6,12,18,7,14,21,5,10,15,6,12,18,7,14,21,8,16,24,7,14,21,8,16,24,9,18,27}
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SortBy[allsigs,((Times@@First[#1]+Times@@First[#2])&@@#)&]
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SortBy[{#,((Times@@First[#1]+Times@@First[#2])&@@#)}&/@allsigs,Last]
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1,1 -> 2,1
1,1 -> 2,1
EnumerateWolframModelRules[{{1,1}}{{2,1}},2]
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{{{1}}{{1},{1}},{{1}}{{1},{2}},{{1}}{{2},{2}},{{1}}{{2},{3}}}
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Select[%,BiConnectedRuleQ]
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{{{1}}{{1},{1}},{{1}}{{2},{2}}}
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WolframModelTest[#,Automatic]&/@%154
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MakePictures[%]
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EnumerateWolframModelRules[{{1,1}}{{2,1}},3]
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{{{1}}{{1},{1}},{{1}}{{1},{2}},{{1}}{{2},{2}},{{1}}{{2},{3}}}
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1,1 -> 3,1
1,1 -> 3,1
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,1}}{{3,1}},4],BiConnectedRuleQ];
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2
»
WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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{10,1,1,15,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
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MakePictures[First/@Values[GroupBy[%,#FinalState&]]]
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1,1 -> 4,1
1,1 -> 4,1
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,1}}{{4,1}},5],BiConnectedRuleQ];
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2
»
WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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{1,1}
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MakePictures[First/@Values[GroupBy[%%,#FinalState&]]]
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2,1 -> 3,1
2,1 -> 3,1
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{2,1}}{{3,1}},5],BiConnectedRuleQ];
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2
»
WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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{1,1}
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MakePictures[First/@Values[GroupBy[%%,#FinalState&]]]
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1,1 -> 5,1
1,1 -> 5,1
1,2 -> 2,2
1,2 -> 2,2
EnumerateWolframModelRules[{{1,2}}{{2,2}},2]
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Select[%,BiConnectedRuleQ]
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WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%162,#FinalState&]//Values
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{10,1,1,3,1,1,1}
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MakePictures[First/@Values[GroupBy[%162,#FinalState&]]]
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EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{2,2}},3],BiConnectedRuleQ];
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56
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WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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{10,1,1,12,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
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MakePictures[First/@Values[GroupBy[%%,#FinalState&]]]
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PrintCells@{{{{1,2}}{{1,2},{2,3}},{{0,0}},8},{{{1,2}}{{2,1},{2,3}},{{0,0}},7}};
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{{{1,2}}{{1,2},{2,3}},{{0,0}},8}
{{{1,2}}{{2,1},{2,3}},{{0,0}},7}
s 4 etc.
s 4 etc.
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{2,2}},4],BiConnectedRuleQ];
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77
»
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{2,2}},5],BiConnectedRuleQ];
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80
»
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{2,2}},6],BiConnectedRuleQ];
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80
»
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{2,2}},5],BiConnectedRuleQ];
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80
»
WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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{10,1,1,15,1,1,2,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1,1}
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MakePictures[First/@Values[GroupBy[%%,#FinalState&]]]
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{{{1,2}}{{3,2}},8}
{{{1,2}}{{3,2}},8}
Note: only going up to 4 symbols, not 8:
EchoFunction[Length]@Select[EnumerateWolframModelRules[{{1,2}}{{3,2}},4],BiConnectedRuleQ];
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397
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WolframModelTest[#,Automatic]&/@%;
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Length/@GroupBy[%,#FinalState&]//Values
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MakePictures[First/@Values[GroupBy[%201,#FinalState&]]]
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PrintCells@{{{{1,1}}{{1,1},{1,2},{2,2}},{{0,0}},7},{{{1,1}}{{1,2},{2,2},{2,2}},{{0,0}},7},{{{1,2}}{{1,1},{1,3},{3,2}},{{0,0}},4},{{{1,2}}{{1,1},{1,2},{3,1}},{{0,0}},4},{{{1,2}}{{1,1},{3,1},{3,2}},{{0,0}},5},{{{1,2}}{{1,2},{1,3},{2,3}},{{0,0}},4},{{{1,2}}{{1,2},{1,3},{3,3}},{{0,0}},5},{{{1,2}}{{1,2},{2,3},{2,3}},{{0,0}},5},{{{1,2}}{{1,2},{2,3},{3,1}},{{0,0}},4},{{{1,2}}{{1,2},{2,3},{4,1}},{{0,0}},4},{{{1,2}}{{1,2},{3,2},{3,3}},{{0,0}},5},{{{1,2}}{{1,3},{1,3},{2,3}},{{0,0}},4},{{{1,2}}{{1,3},{1,3},{3,2}},{{0,0}},5},{{{1,2}}{{1,3},{1,4},{3,2}},{{0,0}},5},{{{1,2}}{{1,3},{1,4},{2,3}},{{0,0}},4},{{{1,2}}{{1,3},{2,3},{3,3}},{{0,0}},5},{{{1,2}}{{1,3},{2,3},{3,4}},{{0,0}},5},{{{1,2}}{{1,3},{2,3},{3,4}},{{0,0}},5}};
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{{{1,1}}{{1,1},{1,2},{2,2}},{{0,0}},7}
{{{1,1}}{{1,2},{2,2},{2,2}},{{0,0}},7}
{{{1,2}}{{1,1},{1,3},{3,2}},{{0,0}},4}
{{{1,2}}{{1,1},{1,2},{3,1}},{{0,0}},4}
{{{1,2}}{{1,1},{3,1},{3,2}},{{0,0}},5}
{{{1,2}}{{1,2},{1,3},{2,3}},{{0,0}},4}
{{{1,2}}{{1,2},{1,3},{3,3}},{{0,0}},5}
{{{1,2}}{{1,2},{2,3},{2,3}},{{0,0}},5}
{{{1,2}}{{1,2},{2,3},{3,1}},{{0,0}},4}
{{{1,2}}{{1,2},{2,3},{4,1}},{{0,0}},4}
{{{1,2}}{{1,2},{3,2},{3,3}},{{0,0}},5}
{{{1,2}}{{1,3},{1,3},{2,3}},{{0,0}},4}
{{{1,2}}{{1,3},{1,3},{3,2}},{{0,0}},5}
{{{1,2}}{{1,3},{1,4},{3,2}},{{0,0}},5}
{{{1,2}}{{1,3},{1,4},{2,3}},{{0,0}},4}
{{{1,2}}{{1,3},{2,3},{3,3}},{{0,0}},5}
{{{1,2}}{{1,3},{2,3},{3,4}},{{0,0}},5}
{{{1,2}}{{1,3},{2,3},{3,4}},{{0,0}},5}