#55 ⟨a, b | aa=a, ab=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. a2 ⇒ a
  2. ab ⇒ a 
# ab:aa=a,ab=a ab
aa=a
ab=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.

203 total

Σ#PresentationMapping
7237⟨a, b | aa=a, aab=a⟩φ(a) = a, φ(b) = b
7261⟨a, b | ab=a, aab=a⟩φ(a) = a, φ(b) = b
7263⟨a, b | ab=a, aba=a⟩φ(a) = a, φ(b) = b
7275⟨a, b | aa=a, ab=aa⟩φ(a) = a, φ(b) = b
8882⟨a, b | aa=a, aaab=a⟩φ(a) = a, φ(b) = b
8926⟨a, b | ab=a, aabb=a⟩φ(a) = a, φ(b) = b
8930⟨a, b | ab=a, abab=a⟩φ(a) = a, φ(b) = b
8932⟨a, b | ab=a, abba=a⟩φ(a) = a, φ(b) = b
8953⟨a, b | aa=a, aaa=ab⟩φ(a) = a, φ(b) = b
8955⟨a, b | aa=a, aab=aa⟩φ(a) = a, φ(b) = b
8997⟨a, b | ab=a, aab=ab⟩φ(a) = a, φ(b) = b
81001⟨a, b | ab=a, aba=ab⟩φ(a) = a, φ(b) = b
81004⟨a, b | ab=a, abb=aa⟩φ(a) = a, φ(b) = b
91576⟨a, b | aaa=aa, aab=a⟩φ(a) = a, φ(b) = b
92022⟨a, b | aab=a, aaab=a⟩φ(a) = a, φ(b) = b
92024⟨a, b | aab=a, aaba=a⟩φ(a) = a, φ(b) = b
92026⟨a, b | aab=a, aabb=a⟩φ(a) = a, φ(b) = b
92028⟨a, b | aab=a, abaa=a⟩φ(a) = a, φ(b) = b
92030⟨a, b | aab=a, abab=a⟩φ(a) = a, φ(b) = b
92032⟨a, b | aab=a, abba=a⟩φ(a) = a, φ(b) = b
92086⟨a, b | aba=a, aaab=a⟩φ(a) = a, φ(b) = b
92092⟨a, b | aba=a, abab=a⟩φ(a) = a, φ(b) = b
92858⟨a, b | aa=a, aaaab=a⟩φ(a) = a, φ(b) = b
92950⟨a, b | ab=a, aabbb=a⟩φ(a) = a, φ(b) = b
92958⟨a, b | ab=a, ababb=a⟩φ(a) = a, φ(b) = b
92962⟨a, b | ab=a, abbab=a⟩φ(a) = a, φ(b) = b
92964⟨a, b | ab=a, abbba=a⟩φ(a) = a, φ(b) = b
93001⟨a, b | aa=a, aaaa=ab⟩φ(a) = a, φ(b) = b
93003⟨a, b | aa=a, aaab=aa⟩φ(a) = a, φ(b) = b
93085⟨a, b | ab=a, aabb=ab⟩φ(a) = a, φ(b) = b
93093⟨a, b | ab=a, abab=ab⟩φ(a) = a, φ(b) = b
93097⟨a, b | ab=a, abba=ab⟩φ(a) = a, φ(b) = b
93100⟨a, b | ab=a, abbb=aa⟩φ(a) = a, φ(b) = b
93136⟨a, b | aa=a, aab=aaa⟩φ(a) = a, φ(b) = b
93176⟨a, b | ab=a, abb=aab⟩φ(a) = a, φ(b) = b
93177⟨a, b | ab=a, abb=aba⟩φ(a) = a, φ(b) = b
105024⟨a, b | aaa=aa, aaab=a⟩φ(a) = a, φ(b) = b
105100⟨a, b | aab=aa, aabb=a⟩φ(a) = a, φ(b) = b
105104⟨a, b | aab=aa, abab=a⟩φ(a) = a, φ(b) = b
105128⟨a, b | aab=ab, aaab=a⟩φ(a) = a, φ(b) = b
105230⟨a, b | aba=aa, abab=a⟩φ(a) = a, φ(b) = b
105244⟨a, b | aba=ab, aaab=a⟩φ(a) = a, φ(b) = b
105246⟨a, b | aba=ab, aaba=a⟩φ(a) = a, φ(b) = b
105250⟨a, b | aba=ab, abaa=a⟩φ(a) = a, φ(b) = b
108570⟨a, b | aa=a, aaaaab=a⟩φ(a) = a, φ(b) = b
108742⟨a, b | ab=a, aabbbb=a⟩φ(a) = a, φ(b) = b
108758⟨a, b | ab=a, ababbb=a⟩φ(a) = a, φ(b) = b
108766⟨a, b | ab=a, abbabb=a⟩φ(a) = a, φ(b) = b
108770⟨a, b | ab=a, abbbab=a⟩φ(a) = a, φ(b) = b
108772⟨a, b | ab=a, abbbba=a⟩φ(a) = a, φ(b) = b
108841⟨a, b | aa=a, aaaaa=ab⟩φ(a) = a, φ(b) = b
108843⟨a, b | aa=a, aaaab=aa⟩φ(a) = a, φ(b) = b
109013⟨a, b | ab=a, aabbb=ab⟩φ(a) = a, φ(b) = b
109029⟨a, b | ab=a, ababb=ab⟩φ(a) = a, φ(b) = b
109037⟨a, b | ab=a, abbab=ab⟩φ(a) = a, φ(b) = b
109041⟨a, b | ab=a, abbba=ab⟩φ(a) = a, φ(b) = b
109044⟨a, b | ab=a, abbbb=aa⟩φ(a) = a, φ(b) = b
109113⟨a, b | aa=a, aaaa=aab⟩φ(a) = a, φ(b) = b
109118⟨a, b | aa=a, aaab=aaa⟩φ(a) = a, φ(b) = b
109283⟨a, b | ab=a, aabb=abb⟩φ(a) = a, φ(b) = b
109299⟨a, b | ab=a, abab=abb⟩φ(a) = a, φ(b) = b
109307⟨a, b | ab=a, abba=abb⟩φ(a) = a, φ(b) = b
109313⟨a, b | ab=a, abbb=aab⟩φ(a) = a, φ(b) = b
109314⟨a, b | ab=a, abbb=aba⟩φ(a) = a, φ(b) = b
1112214⟨a, b | aaab=aa, aaba=a⟩φ(a) = a, φ(b) = b
1112216⟨a, b | aaab=aa, aabb=a⟩φ(a) = a, φ(b) = b
1112218⟨a, b | aaab=aa, abaa=a⟩φ(a) = a, φ(b) = b
1112220⟨a, b | aaab=aa, abab=a⟩φ(a) = a, φ(b) = b
1112330⟨a, b | aaba=aa, abab=a⟩φ(a) = a, φ(b) = b
1112456⟨a, b | aabb=ab, abab=a⟩φ(a) = a, φ(b) = b
1114411⟨a, b | aaab=a, aaaab=a⟩φ(a) = a, φ(b) = b
1114413⟨a, b | aaab=a, aaaba=a⟩φ(a) = a, φ(b) = b
1114417⟨a, b | aaab=a, aabaa=a⟩φ(a) = a, φ(b) = b
1114425⟨a, b | aaab=a, abaaa=a⟩φ(a) = a, φ(b) = b
1114539⟨a, b | aaba=a, aaaab=a⟩φ(a) = a, φ(b) = b
1114679⟨a, b | aabb=a, aabbb=a⟩φ(a) = a, φ(b) = b
1114691⟨a, b | aabb=a, abbab=a⟩φ(a) = a, φ(b) = b
1114743⟨a, b | abab=a, aabbb=a⟩φ(a) = a, φ(b) = b
1114751⟨a, b | abab=a, ababb=a⟩φ(a) = a, φ(b) = b
1114755⟨a, b | abab=a, abbab=a⟩φ(a) = a, φ(b) = b
1114757⟨a, b | abab=a, abbba=a⟩φ(a) = a, φ(b) = b
1114815⟨a, b | abba=a, abbab=a⟩φ(a) = a, φ(b) = b
1115403⟨a, b | aaa=aa, aaaab=a⟩φ(a) = a, φ(b) = b
1115559⟨a, b | aab=aa, aabbb=a⟩φ(a) = a, φ(b) = b
1115571⟨a, b | aab=aa, abbab=a⟩φ(a) = a, φ(b) = b
1115611⟨a, b | aab=ab, aaaab=a⟩φ(a) = a, φ(b) = b
1115823⟨a, b | aba=aa, abbab=a⟩φ(a) = a, φ(b) = b
1115843⟨a, b | aba=ab, aaaab=a⟩φ(a) = a, φ(b) = b
1115845⟨a, b | aba=ab, aaaba=a⟩φ(a) = a, φ(b) = b
1115849⟨a, b | aba=ab, aabaa=a⟩φ(a) = a, φ(b) = b
1115857⟨a, b | aba=ab, abaaa=a⟩φ(a) = a, φ(b) = b
1118838⟨a, b | aab=a, aaaabb=a⟩φ(a) = a, φ(b) = b
1118842⟨a, b | aab=a, aaabab=a⟩φ(a) = a, φ(b) = b
1118844⟨a, b | aab=a, aaabba=a⟩φ(a) = a, φ(b) = b
1118846⟨a, b | aab=a, aaabbb=a⟩φ(a) = a, φ(b) = b
1118850⟨a, b | aab=a, aabaab=a⟩φ(a) = a, φ(b) = b
1118852⟨a, b | aab=a, aababa=a⟩φ(a) = a, φ(b) = b
1118854⟨a, b | aab=a, aababb=a⟩φ(a) = a, φ(b) = b
1118856⟨a, b | aab=a, aabbaa=a⟩φ(a) = a, φ(b) = b
1118858⟨a, b | aab=a, aabbab=a⟩φ(a) = a, φ(b) = b
1118860⟨a, b | aab=a, aabbba=a⟩φ(a) = a, φ(b) = b
1118866⟨a, b | aab=a, abaaab=a⟩φ(a) = a, φ(b) = b
1118868⟨a, b | aab=a, abaaba=a⟩φ(a) = a, φ(b) = b
1118870⟨a, b | aab=a, abaabb=a⟩φ(a) = a, φ(b) = b
1118872⟨a, b | aab=a, ababaa=a⟩φ(a) = a, φ(b) = b
1118874⟨a, b | aab=a, ababab=a⟩φ(a) = a, φ(b) = b
1118876⟨a, b | aab=a, ababba=a⟩φ(a) = a, φ(b) = b
1118880⟨a, b | aab=a, abbaaa=a⟩φ(a) = a, φ(b) = b
1118882⟨a, b | aab=a, abbaab=a⟩φ(a) = a, φ(b) = b
1118884⟨a, b | aab=a, abbaba=a⟩φ(a) = a, φ(b) = b
1118888⟨a, b | aab=a, abbbaa=a⟩φ(a) = a, φ(b) = b
1119098⟨a, b | aba=a, aaabab=a⟩φ(a) = a, φ(b) = b
1119104⟨a, b | aba=a, aabaab=a⟩φ(a) = a, φ(b) = b
1119112⟨a, b | aba=a, aabbab=a⟩φ(a) = a, φ(b) = b
1119118⟨a, b | aba=a, abaaab=a⟩φ(a) = a, φ(b) = b
1119124⟨a, b | aba=a, ababab=a⟩φ(a) = a, φ(b) = b
1119130⟨a, b | aba=a, abbaab=a⟩φ(a) = a, φ(b) = b
1119380⟨a, b | aab=a, aaaab=aa⟩φ(a) = a, φ(b) = b
1119384⟨a, b | aab=a, aaaba=aa⟩φ(a) = a, φ(b) = b
1119388⟨a, b | aab=a, aaabb=aa⟩φ(a) = a, φ(b) = b
1119389⟨a, b | aab=a, aaabb=ab⟩φ(a) = a, φ(b) = b
1119392⟨a, b | aab=a, aabaa=aa⟩φ(a) = a, φ(b) = b
1119396⟨a, b | aab=a, aabab=aa⟩φ(a) = a, φ(b) = b
1119397⟨a, b | aab=a, aabab=ab⟩φ(a) = a, φ(b) = b
1119400⟨a, b | aab=a, aabba=aa⟩φ(a) = a, φ(b) = b
1119401⟨a, b | aab=a, aabba=ab⟩φ(a) = a, φ(b) = b
1119405⟨a, b | aab=a, aabbb=ab⟩φ(a) = a, φ(b) = b
1119408⟨a, b | aab=a, abaaa=aa⟩φ(a) = a, φ(b) = b
1119412⟨a, b | aab=a, abaab=aa⟩φ(a) = a, φ(b) = b
1119413⟨a, b | aab=a, abaab=ab⟩φ(a) = a, φ(b) = b
1119416⟨a, b | aab=a, ababa=aa⟩φ(a) = a, φ(b) = b
1119417⟨a, b | aab=a, ababa=ab⟩φ(a) = a, φ(b) = b
1119421⟨a, b | aab=a, ababb=ab⟩φ(a) = a, φ(b) = b
1119424⟨a, b | aab=a, abbaa=aa⟩φ(a) = a, φ(b) = b
1119425⟨a, b | aab=a, abbaa=ab⟩φ(a) = a, φ(b) = b
1119429⟨a, b | aab=a, abbab=ab⟩φ(a) = a, φ(b) = b
1119433⟨a, b | aab=a, abbba=ab⟩φ(a) = a, φ(b) = b
1119446⟨a, b | aab=a, baaab=ba⟩φ(a) = a, φ(b) = b
1119450⟨a, b | aab=a, baaba=ba⟩φ(a) = a, φ(b) = b
1119454⟨a, b | aab=a, baabb=ba⟩φ(a) = a, φ(b) = b
1119458⟨a, b | aab=a, babaa=ba⟩φ(a) = a, φ(b) = b
1119462⟨a, b | aab=a, babab=ba⟩φ(a) = a, φ(b) = b
1119466⟨a, b | aab=a, babba=ba⟩φ(a) = a, φ(b) = b
1119655⟨a, b | aba=a, aabba=ab⟩φ(a) = a, φ(b) = b
1119667⟨a, b | aba=a, ababa=ab⟩φ(a) = a, φ(b) = b
1119678⟨a, b | aba=a, abbba=ab⟩φ(a) = a, φ(b) = b
1119920⟨a, b | aab=a, aaaa=aaa⟩φ(a) = a, φ(b) = b
1119928⟨a, b | aab=a, aaab=aaa⟩φ(a) = a, φ(b) = b
1119929⟨a, b | aab=a, aaab=aab⟩φ(a) = a, φ(b) = b
1119930⟨a, b | aab=a, aaab=aba⟩φ(a) = a, φ(b) = b
1119936⟨a, b | aab=a, aaba=aaa⟩φ(a) = a, φ(b) = b
1119937⟨a, b | aab=a, aaba=aab⟩φ(a) = a, φ(b) = b
1119938⟨a, b | aab=a, aaba=aba⟩φ(a) = a, φ(b) = b
1119945⟨a, b | aab=a, aabb=aab⟩φ(a) = a, φ(b) = b
1119946⟨a, b | aab=a, aabb=aba⟩φ(a) = a, φ(b) = b
1119947⟨a, b | aab=a, aabb=abb⟩φ(a) = a, φ(b) = b
1119952⟨a, b | aab=a, abaa=aaa⟩φ(a) = a, φ(b) = b
1119953⟨a, b | aab=a, abaa=aab⟩φ(a) = a, φ(b) = b
1119954⟨a, b | aab=a, abaa=aba⟩φ(a) = a, φ(b) = b
1119961⟨a, b | aab=a, abab=aab⟩φ(a) = a, φ(b) = b
1119962⟨a, b | aab=a, abab=aba⟩φ(a) = a, φ(b) = b
1119963⟨a, b | aab=a, abab=abb⟩φ(a) = a, φ(b) = b
1119969⟨a, b | aab=a, abba=aab⟩φ(a) = a, φ(b) = b
1119970⟨a, b | aab=a, abba=aba⟩φ(a) = a, φ(b) = b
1119971⟨a, b | aab=a, abba=abb⟩φ(a) = a, φ(b) = b
1119979⟨a, b | aab=a, abbb=abb⟩φ(a) = a, φ(b) = b
1119988⟨a, b | aab=a, baaa=baa⟩φ(a) = a, φ(b) = b
1119996⟨a, b | aab=a, baab=baa⟩φ(a) = a, φ(b) = b
1119997⟨a, b | aab=a, baab=bab⟩φ(a) = a, φ(b) = b
1120004⟨a, b | aab=a, baba=baa⟩φ(a) = a, φ(b) = b
1120005⟨a, b | aab=a, baba=bab⟩φ(a) = a, φ(b) = b
1120013⟨a, b | aab=a, babb=bab⟩φ(a) = a, φ(b) = b
1120022⟨a, b | aab=a, bbaa=bba⟩φ(a) = a, φ(b) = b
1120030⟨a, b | aab=a, bbab=bba⟩φ(a) = a, φ(b) = b
1120184⟨a, b | aba=a, aaab=aba⟩φ(a) = a, φ(b) = b
1120208⟨a, b | aba=a, abab=aba⟩φ(a) = a, φ(b) = b
1124046⟨a, b | aa=a, aaaaaab=a⟩φ(a) = a, φ(b) = b
1124394⟨a, b | ab=a, aabbbbb=a⟩φ(a) = a, φ(b) = b
1124426⟨a, b | ab=a, ababbbb=a⟩φ(a) = a, φ(b) = b
1124442⟨a, b | ab=a, abbabbb=a⟩φ(a) = a, φ(b) = b
1124450⟨a, b | ab=a, abbbabb=a⟩φ(a) = a, φ(b) = b
1124454⟨a, b | ab=a, abbbbab=a⟩φ(a) = a, φ(b) = b
1124456⟨a, b | ab=a, abbbbba=a⟩φ(a) = a, φ(b) = b
1124589⟨a, b | aa=a, aaaaaa=ab⟩φ(a) = a, φ(b) = b
1124591⟨a, b | aa=a, aaaaab=aa⟩φ(a) = a, φ(b) = b
1124921⟨a, b | ab=a, aabbbb=ab⟩φ(a) = a, φ(b) = b
1124953⟨a, b | ab=a, ababbb=ab⟩φ(a) = a, φ(b) = b
1124969⟨a, b | ab=a, abbabb=ab⟩φ(a) = a, φ(b) = b
1124977⟨a, b | ab=a, abbbab=ab⟩φ(a) = a, φ(b) = b
1124981⟨a, b | ab=a, abbbba=ab⟩φ(a) = a, φ(b) = b
1124984⟨a, b | ab=a, abbbbb=aa⟩φ(a) = a, φ(b) = b
1125117⟨a, b | aa=a, aaaaa=aab⟩φ(a) = a, φ(b) = b
1125122⟨a, b | aa=a, aaaab=aaa⟩φ(a) = a, φ(b) = b
1125463⟨a, b | ab=a, aabbb=abb⟩φ(a) = a, φ(b) = b
1125495⟨a, b | ab=a, ababb=abb⟩φ(a) = a, φ(b) = b
1125511⟨a, b | ab=a, abbab=abb⟩φ(a) = a, φ(b) = b
1125519⟨a, b | ab=a, abbba=abb⟩φ(a) = a, φ(b) = b
1125525⟨a, b | ab=a, abbbb=aab⟩φ(a) = a, φ(b) = b
1125526⟨a, b | ab=a, abbbb=aba⟩φ(a) = a, φ(b) = b
1125660⟨a, b | aa=a, aaab=aaaa⟩φ(a) = a, φ(b) = b
1125816⟨a, b | ab=a, abbb=aabb⟩φ(a) = a, φ(b) = b
1125818⟨a, b | ab=a, abbb=abab⟩φ(a) = a, φ(b) = b
1125819⟨a, b | ab=a, abbb=abba⟩φ(a) = a, φ(b) = b

Other anti-isomorphic instances

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

18 total

Σ#PresentationMapping
91626⟨a, b | aab=ab, baa=a⟩φ(a) = a, φ(b) = b
91660⟨a, b | aba=aa, baa=a⟩φ(a) = a, φ(b) = b
91676⟨a, b | aba=ba, baa=a⟩φ(a) = a, φ(b) = b
105142⟨a, b | aab=ab, baaa=a⟩φ(a) = a, φ(b) = b
1112336⟨a, b | aaba=aa, baaa=a⟩φ(a) = a, φ(b) = b
1112340⟨a, b | aaba=aa, baba=a⟩φ(a) = a, φ(b) = b
1112490⟨a, b | abaa=aa, baaa=a⟩φ(a) = a, φ(b) = b
1112522⟨a, b | abab=ab, baaa=a⟩φ(a) = a, φ(b) = b
1112524⟨a, b | abab=ab, baba=a⟩φ(a) = a, φ(b) = b
1112586⟨a, b | abba=ba, baaa=a⟩φ(a) = a, φ(b) = b
1112588⟨a, b | abba=ba, baba=a⟩φ(a) = a, φ(b) = b
1112590⟨a, b | abba=ba, bbaa=a⟩φ(a) = a, φ(b) = b
1114569⟨a, b | aaba=a, baaaa=a⟩φ(a) = a, φ(b) = b
1115641⟨a, b | aab=ab, baaaa=a⟩φ(a) = a, φ(b) = b
1119656⟨a, b | aba=a, aabba=ba⟩φ(a) = a, φ(b) = b
1119685⟨a, b | aba=a, baaab=ab⟩φ(a) = a, φ(b) = b
1119692⟨a, b | aba=a, babab=ab⟩φ(a) = a, φ(b) = b
1120211⟨a, b | aba=a, abab=bab⟩φ(a) = a, φ(b) = b