#259 ⟨a, b | ab=a, aaa=a⟩

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Properties

Complete rewriting system

Format:
Word to reduce:
Tips:
  • Lowercase letters stand for generators.
  • Spaces are ignored.
  • Numbers repeat the previous letter, e.g. b90.
Reduction strategy:
Path to normal form: 1 
1
  1. ab ⇒ a
  2. a3 ⇒ a 
# ab:ab=a,aaa=a ab
ab=a
aaa=a

Right Cayley graph (truncated)

Left Cayley graph (truncated)

Other isomorphic instances

The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.

105 total

Σ#PresentationMapping
8922⟨a, b | ab=a, aaab=a⟩φ(a) = a, φ(b) = b
8924⟨a, b | ab=a, aaba=a⟩φ(a) = a, φ(b) = b
8928⟨a, b | ab=a, abaa=a⟩φ(a) = a, φ(b) = b
8993⟨a, b | ab=a, aaa=ab⟩φ(a) = a, φ(b) = b
91982⟨a, b | aaa=a, aaab=a⟩φ(a) = a, φ(b) = b
92942⟨a, b | ab=a, aaabb=a⟩φ(a) = a, φ(b) = b
92946⟨a, b | ab=a, aabab=a⟩φ(a) = a, φ(b) = b
92948⟨a, b | ab=a, aabba=a⟩φ(a) = a, φ(b) = b
92954⟨a, b | ab=a, abaab=a⟩φ(a) = a, φ(b) = b
92956⟨a, b | ab=a, ababa=a⟩φ(a) = a, φ(b) = b
92960⟨a, b | ab=a, abbaa=a⟩φ(a) = a, φ(b) = b
93077⟨a, b | ab=a, aaab=ab⟩φ(a) = a, φ(b) = b
93081⟨a, b | ab=a, aaba=ab⟩φ(a) = a, φ(b) = b
93089⟨a, b | ab=a, abaa=ab⟩φ(a) = a, φ(b) = b
93175⟨a, b | ab=a, abb=aaa⟩φ(a) = a, φ(b) = b
105096⟨a, b | aab=aa, aaab=a⟩φ(a) = a, φ(b) = b
105098⟨a, b | aab=aa, aaba=a⟩φ(a) = a, φ(b) = b
105102⟨a, b | aab=aa, abaa=a⟩φ(a) = a, φ(b) = b
105224⟨a, b | aba=aa, aaab=a⟩φ(a) = a, φ(b) = b
105265⟨a, b | aba=ab, babb=b⟩φ(a) = b, φ(b) = a
105269⟨a, b | aba=ab, bbab=b⟩φ(a) = b, φ(b) = a
105271⟨a, b | aba=ab, bbba=b⟩φ(a) = b, φ(b) = a
108726⟨a, b | ab=a, aaabbb=a⟩φ(a) = a, φ(b) = b
108734⟨a, b | ab=a, aababb=a⟩φ(a) = a, φ(b) = b
108738⟨a, b | ab=a, aabbab=a⟩φ(a) = a, φ(b) = b
108740⟨a, b | ab=a, aabbba=a⟩φ(a) = a, φ(b) = b
108750⟨a, b | ab=a, abaabb=a⟩φ(a) = a, φ(b) = b
108754⟨a, b | ab=a, ababab=a⟩φ(a) = a, φ(b) = b
108756⟨a, b | ab=a, ababba=a⟩φ(a) = a, φ(b) = b
108762⟨a, b | ab=a, abbaab=a⟩φ(a) = a, φ(b) = b
108764⟨a, b | ab=a, abbaba=a⟩φ(a) = a, φ(b) = b
108768⟨a, b | ab=a, abbbaa=a⟩φ(a) = a, φ(b) = b
108997⟨a, b | ab=a, aaabb=ab⟩φ(a) = a, φ(b) = b
109005⟨a, b | ab=a, aabab=ab⟩φ(a) = a, φ(b) = b
109009⟨a, b | ab=a, aabba=ab⟩φ(a) = a, φ(b) = b
109021⟨a, b | ab=a, abaab=ab⟩φ(a) = a, φ(b) = b
109025⟨a, b | ab=a, ababa=ab⟩φ(a) = a, φ(b) = b
109033⟨a, b | ab=a, abbaa=ab⟩φ(a) = a, φ(b) = b
109267⟨a, b | ab=a, aaab=abb⟩φ(a) = a, φ(b) = b
109275⟨a, b | ab=a, aaba=abb⟩φ(a) = a, φ(b) = b
109291⟨a, b | ab=a, abaa=abb⟩φ(a) = a, φ(b) = b
109312⟨a, b | ab=a, abbb=aaa⟩φ(a) = a, φ(b) = b
1112148⟨a, b | aaaa=aa, aaab=a⟩φ(a) = a, φ(b) = b
1112354⟨a, b | aaba=ab, abaa=a⟩φ(a) = a, φ(b) = b
1114415⟨a, b | aaab=a, aaabb=a⟩φ(a) = a, φ(b) = b
1114419⟨a, b | aaab=a, aabab=a⟩φ(a) = a, φ(b) = b
1114421⟨a, b | aaab=a, aabba=a⟩φ(a) = a, φ(b) = b
1114427⟨a, b | aaab=a, abaab=a⟩φ(a) = a, φ(b) = b
1114429⟨a, b | aaab=a, ababa=a⟩φ(a) = a, φ(b) = b
1114433⟨a, b | aaab=a, abbaa=a⟩φ(a) = a, φ(b) = b
1114547⟨a, b | aaba=a, aabab=a⟩φ(a) = a, φ(b) = b
1114555⟨a, b | aaba=a, abaab=a⟩φ(a) = a, φ(b) = b
1115551⟨a, b | aab=aa, aaabb=a⟩φ(a) = a, φ(b) = b
1115555⟨a, b | aab=aa, aabab=a⟩φ(a) = a, φ(b) = b
1115557⟨a, b | aab=aa, aabba=a⟩φ(a) = a, φ(b) = b
1115563⟨a, b | aab=aa, abaab=a⟩φ(a) = a, φ(b) = b
1115569⟨a, b | aab=aa, abbaa=a⟩φ(a) = a, φ(b) = b
1115811⟨a, b | aba=aa, aabab=a⟩φ(a) = a, φ(b) = b
1115817⟨a, b | aba=aa, abaab=a⟩φ(a) = a, φ(b) = b
1115880⟨a, b | aba=ab, baabb=b⟩φ(a) = b, φ(b) = a
1115884⟨a, b | aba=ab, babab=b⟩φ(a) = b, φ(b) = a
1115886⟨a, b | aba=ab, babba=b⟩φ(a) = b, φ(b) = a
1115892⟨a, b | aba=ab, bbaab=b⟩φ(a) = b, φ(b) = a
1115894⟨a, b | aba=ab, bbaba=b⟩φ(a) = b, φ(b) = a
1115898⟨a, b | aba=ab, bbbaa=b⟩φ(a) = b, φ(b) = a
1118690⟨a, b | aaa=a, aaaaab=a⟩φ(a) = a, φ(b) = b
1119233⟨a, b | aaa=a, aaaaa=ab⟩φ(a) = a, φ(b) = b
1119235⟨a, b | aaa=a, aaaab=aa⟩φ(a) = a, φ(b) = b
1119777⟨a, b | aaa=a, aaaa=aab⟩φ(a) = a, φ(b) = b
1119782⟨a, b | aaa=a, aaab=aaa⟩φ(a) = a, φ(b) = b
1124362⟨a, b | ab=a, aaabbbb=a⟩φ(a) = a, φ(b) = b
1124378⟨a, b | ab=a, aababbb=a⟩φ(a) = a, φ(b) = b
1124386⟨a, b | ab=a, aabbabb=a⟩φ(a) = a, φ(b) = b
1124390⟨a, b | ab=a, aabbbab=a⟩φ(a) = a, φ(b) = b
1124392⟨a, b | ab=a, aabbbba=a⟩φ(a) = a, φ(b) = b
1124410⟨a, b | ab=a, abaabbb=a⟩φ(a) = a, φ(b) = b
1124418⟨a, b | ab=a, abababb=a⟩φ(a) = a, φ(b) = b
1124422⟨a, b | ab=a, ababbab=a⟩φ(a) = a, φ(b) = b
1124424⟨a, b | ab=a, ababbba=a⟩φ(a) = a, φ(b) = b
1124434⟨a, b | ab=a, abbaabb=a⟩φ(a) = a, φ(b) = b
1124438⟨a, b | ab=a, abbabab=a⟩φ(a) = a, φ(b) = b
1124440⟨a, b | ab=a, abbabba=a⟩φ(a) = a, φ(b) = b
1124446⟨a, b | ab=a, abbbaab=a⟩φ(a) = a, φ(b) = b
1124448⟨a, b | ab=a, abbbaba=a⟩φ(a) = a, φ(b) = b
1124452⟨a, b | ab=a, abbbbaa=a⟩φ(a) = a, φ(b) = b
1124889⟨a, b | ab=a, aaabbb=ab⟩φ(a) = a, φ(b) = b
1124905⟨a, b | ab=a, aababb=ab⟩φ(a) = a, φ(b) = b
1124913⟨a, b | ab=a, aabbab=ab⟩φ(a) = a, φ(b) = b
1124917⟨a, b | ab=a, aabbba=ab⟩φ(a) = a, φ(b) = b
1124937⟨a, b | ab=a, abaabb=ab⟩φ(a) = a, φ(b) = b
1124945⟨a, b | ab=a, ababab=ab⟩φ(a) = a, φ(b) = b
1124949⟨a, b | ab=a, ababba=ab⟩φ(a) = a, φ(b) = b
1124961⟨a, b | ab=a, abbaab=ab⟩φ(a) = a, φ(b) = b
1124965⟨a, b | ab=a, abbaba=ab⟩φ(a) = a, φ(b) = b
1124973⟨a, b | ab=a, abbbaa=ab⟩φ(a) = a, φ(b) = b
1125431⟨a, b | ab=a, aaabb=abb⟩φ(a) = a, φ(b) = b
1125447⟨a, b | ab=a, aabab=abb⟩φ(a) = a, φ(b) = b
1125455⟨a, b | ab=a, aabba=abb⟩φ(a) = a, φ(b) = b
1125479⟨a, b | ab=a, abaab=abb⟩φ(a) = a, φ(b) = b
1125487⟨a, b | ab=a, ababa=abb⟩φ(a) = a, φ(b) = b
1125503⟨a, b | ab=a, abbaa=abb⟩φ(a) = a, φ(b) = b
1125524⟨a, b | ab=a, abbbb=aaa⟩φ(a) = a, φ(b) = b
1125814⟨a, b | ab=a, abbb=aaab⟩φ(a) = a, φ(b) = b
1125815⟨a, b | ab=a, abbb=aaba⟩φ(a) = a, φ(b) = b
1125817⟨a, b | ab=a, abbb=abaa⟩φ(a) = a, φ(b) = b