#1328 ⟨a, b | aaaa=b, abbb=1⟩

Properties

Element profile

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. a13 ⇒ 1
  2. ba4
# ab:aaaa=b,abbb=1 a/b
aaaaaaaaaaaaa=1
b=aaaa

Staircase diagram

Cayley table

1aa2a3a4a5a6a7a8a9a10a11a12
11aa2a3a4a5a6a7a8a9a10a11a12
aaa2a3a4a5a6a7a8a9a10a11a121
a2a2a3a4a5a6a7a8a9a10a11a121a
a3a3a4a5a6a7a8a9a10a11a121aa2
a4a4a5a6a7a8a9a10a11a121aa2a3
a5a5a6a7a8a9a10a11a121aa2a3a4
a6a6a7a8a9a10a11a121aa2a3a4a5
a7a7a8a9a10a11a121aa2a3a4a5a6
a8a8a9a10a11a121aa2a3a4a5a6a7
a9a9a10a11a121aa2a3a4a5a6a7a8
a10a10a11a121aa2a3a4a5a6a7a8a9
a11a11a121aa2a3a4a5a6a7a8a9a10
a12a121aa2a3a4a5a6a7a8a9a10a11

Right Cayley graph

Others with same cardinality

26 unique, 114 total

Σ#PresentationDescriptionRelated
92118a, b | aba=b, baab=aFinite non-commutative monoid with 13 elements4 iso
104642a, b | aaaa=b, abbb=aIsomorphic to ℕ(13 = 1)10 iso
104643a, b | aaaa=b, abbb=bIsomorphic to ℕ(13 = 4)6 iso
104683a, b | aaab=b, abba=aFinite non-commutative monoid with 13 elements15 iso, 1 anti-iso
105065a, b | aaa=ab, babb=bFinite non-commutative monoid with 13 elements7 iso
105334a, b | aaa=ab, bba=bbFinite non-commutative monoid with 13 elements
105336a, b | aaa=ab, bbb=abFinite non-commutative monoid with 13 elements1 iso
105337a, b | aaa=ab, bbb=baFinite non-commutative monoid with 13 elements
105340a, b | aaa=bb, aab=baFinite non-commutative monoid with 13 elements
106305a, b | aaa=b, abbbb=bIsomorphic to ℕ(13 = 3)2 iso
107143a, b | bb=aa, aaab=baFinite non-commutative monoid with 13 elements1 iso
1112240a, b | aaab=aa, bbbb=aIsomorphic to ℕ(13 = 8)1 iso
1112268a, b | aaab=ab, bbbb=aIsomorphic to ℕ(13 = 5)3 iso
1112324a, b | aaab=bb, bbbb=aIsomorphic to ℕ(13 = 2)14 iso
1114647a, b | aaba=b, babbb=aFinite commutative monoid with 13 elements2 iso
1115520a, b | aaa=bb, aabbb=bFinite commutative monoid with 13 elements2 iso
1116012a, b | aaa=ab, abbb=bbFinite non-commutative monoid with 13 elements
1116069a, b | aaa=bb, abbb=baFinite non-commutative monoid with 13 elements1 anti-iso
1116205a, b | aab=ab, bbbb=aaFinite non-commutative monoid with 13 elements1 iso, 1 anti-iso
1116459a, b | aba=bb, abbb=aaFinite non-commutative monoid with 13 elements1 iso
1116506a, b | aab=ab, bbb=aaaFinite non-commutative monoid with 13 elements1 iso
1116515a, b | aab=ba, bbb=aaaFinite non-commutative monoid with 13 elements
1118958a, b | aab=a, bbbbbb=aIsomorphic to ℕ(13 = 6)4 iso
1120046a, b | aab=a, bbbb=bbaFinite non-commutative monoid with 13 elements
1120927a, b | ab=aa, aaaa=bbbFinite non-commutative monoid with 13 elements7 iso
1120991a, b | ab=aa, baaa=bbbFinite non-commutative monoid with 13 elements3 iso

Other isomorphic instances

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

189 total

Σ#PresentationMapping
91330a, b | aaaa=b, babb=1⟩φ(a) = bbbbbbbbbb, φ(b) = b
91869a, b | aaa=b, abbbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
91873a, b | aaa=b, babbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
91874a, b | aaa=b, bbabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
104809a, b | aaa=bb, aabbb=1⟩φ(a) = bbbbb, φ(b) = b
104812a, b | aaa=bb, ababb=1⟩φ(a) = bbbbb, φ(b) = b
104813a, b | aaa=bb, abbab=1⟩φ(a) = bbbbb, φ(b) = b
104814a, b | aaa=bb, abbba=1⟩φ(a) = bbbbb, φ(b) = b
104817a, b | aaa=bb, baabb=1⟩φ(a) = bbbbb, φ(b) = b
104818a, b | aaa=bb, babab=1⟩φ(a) = bbbbb, φ(b) = b
107678a, b | aab=1, bbbbbb=aφ(a) = bbbbbb, φ(b) = b
107750a, b | aba=1, bbbbbb=aφ(a) = bbbbbb, φ(b) = b
108419a, b | aa=b, abbbbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
108433a, b | aa=b, babbbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
108437a, b | aa=b, bbabbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
108438a, b | aa=b, bbbabbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1110661a, b | aaaa=bbb, aaab=1⟩φ(a) = bbbb, φ(b) = b
1110662a, b | aaaa=bbb, aaba=1⟩φ(a) = bbbb, φ(b) = b
1111117a, b | aaaaa=b, aaabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111119a, b | aaaaa=b, aabab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111120a, b | aaaaa=b, aabba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111122a, b | aaaaa=b, abaab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111123a, b | aaaaa=b, ababa=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111128a, b | aaaaa=b, baaab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1111655a, b | aaaa=ab, abbbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111663a, b | aaaa=ab, babbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111667a, b | aaaa=ab, bbabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111669a, b | aaaa=ab, bbbab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111670a, b | aaaa=ab, bbbba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111803a, b | aaab=bb, abbbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111811a, b | aaab=bb, babbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111815a, b | aaab=bb, bbabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111817a, b | aaab=bb, bbbab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111818a, b | aaab=bb, bbbba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111931a, b | aaba=bb, abbbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111939a, b | aaba=bb, babbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111943a, b | aaba=bb, bbabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111945a, b | aaba=bb, bbbab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1111946a, b | aaba=bb, bbbba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1113468a, b | aaabb=1, abbbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113484a, b | aaabb=1, babbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113492a, b | aaabb=1, bbabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113496a, b | aaabb=1, bbbabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113498a, b | aaabb=1, bbbbab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113499a, b | aaabb=1, bbbbba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113568a, b | aabab=1, abbbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113584a, b | aabab=1, babbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113592a, b | aabab=1, bbabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113596a, b | aabab=1, bbbabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113598a, b | aabab=1, bbbbab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113599a, b | aabab=1, bbbbba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113632a, b | aabba=1, abbbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113648a, b | aabba=1, babbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113656a, b | aabba=1, bbabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113660a, b | aabba=1, bbbabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113662a, b | aabba=1, bbbbab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113663a, b | aabba=1, bbbbba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113696a, b | abaab=1, abbbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113712a, b | abaab=1, babbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113720a, b | abaab=1, bbabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113724a, b | abaab=1, bbbabb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113726a, b | abaab=1, bbbbab=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113727a, b | abaab=1, bbbbba=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113754a, b | ababa=1, abbbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113761a, b | ababa=1, babbbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113763a, b | ababa=1, bbabbb=1⟩φ(a) = bbbbbbbb, φ(b) = b
1113766a, b | abbba=1, aaaaab=1⟩φ(a) = bbbbb, φ(b) = b
1113767a, b | abbba=1, aaaaba=1⟩φ(a) = bbbbb, φ(b) = b
1113769a, b | abbba=1, aaabaa=1⟩φ(a) = bbbbb, φ(b) = b
1114974a, b | aaa=bb, aaaaab=1⟩φ(a) = bbbbb, φ(b) = b
1114975a, b | aaa=bb, aaaaba=1⟩φ(a) = bbbbb, φ(b) = b
1114977a, b | aaa=bb, aaabaa=1⟩φ(a) = bbbbb, φ(b) = b
1116663a, b | aaab=1, aabbbbb=1⟩φ(a) = bbbb, φ(b) = b
1116679a, b | aaab=1, ababbbb=1⟩φ(a) = bbbb, φ(b) = b
1116687a, b | aaab=1, abbabbb=1⟩φ(a) = bbbb, φ(b) = b
1116691a, b | aaab=1, abbbabb=1⟩φ(a) = bbbb, φ(b) = b
1116693a, b | aaab=1, abbbbab=1⟩φ(a) = bbbb, φ(b) = b
1116694a, b | aaab=1, abbbbba=1⟩φ(a) = bbbb, φ(b) = b
1116711a, b | aaab=1, baabbbb=1⟩φ(a) = bbbb, φ(b) = b
1116719a, b | aaab=1, bababbb=1⟩φ(a) = bbbb, φ(b) = b
1116723a, b | aaab=1, babbabb=1⟩φ(a) = bbbb, φ(b) = b
1116725a, b | aaab=1, babbbab=1⟩φ(a) = bbbb, φ(b) = b
1116726a, b | aaab=1, babbbba=1⟩φ(a) = bbbb, φ(b) = b
1116735a, b | aaab=1, bbaabbb=1⟩φ(a) = bbbb, φ(b) = b
1116739a, b | aaab=1, bbababb=1⟩φ(a) = bbbb, φ(b) = b
1116741a, b | aaab=1, bbabbab=1⟩φ(a) = bbbb, φ(b) = b
1116742a, b | aaab=1, bbabbba=1⟩φ(a) = bbbb, φ(b) = b
1116747a, b | aaab=1, bbbaabb=1⟩φ(a) = bbbb, φ(b) = b
1116749a, b | aaab=1, bbbabab=1⟩φ(a) = bbbb, φ(b) = b
1116750a, b | aaab=1, bbbabba=1⟩φ(a) = bbbb, φ(b) = b
1116753a, b | aaab=1, bbbbaab=1⟩φ(a) = bbbb, φ(b) = b
1116754a, b | aaab=1, bbbbaba=1⟩φ(a) = bbbb, φ(b) = b
1116756a, b | aaab=1, bbbbbaa=1⟩φ(a) = bbbb, φ(b) = b
1116791a, b | aaba=1, aabbbbb=1⟩φ(a) = bbbb, φ(b) = b
1116807a, b | aaba=1, ababbbb=1⟩φ(a) = bbbb, φ(b) = b
1116815a, b | aaba=1, abbabbb=1⟩φ(a) = bbbb, φ(b) = b
1116819a, b | aaba=1, abbbabb=1⟩φ(a) = bbbb, φ(b) = b
1116821a, b | aaba=1, abbbbab=1⟩φ(a) = bbbb, φ(b) = b
1116822a, b | aaba=1, abbbbba=1⟩φ(a) = bbbb, φ(b) = b
1116839a, b | aaba=1, baabbbb=1⟩φ(a) = bbbb, φ(b) = b
1116847a, b | aaba=1, bababbb=1⟩φ(a) = bbbb, φ(b) = b
1116851a, b | aaba=1, babbabb=1⟩φ(a) = bbbb, φ(b) = b
1116853a, b | aaba=1, babbbab=1⟩φ(a) = bbbb, φ(b) = b
1116854a, b | aaba=1, babbbba=1⟩φ(a) = bbbb, φ(b) = b
1116863a, b | aaba=1, bbaabbb=1⟩φ(a) = bbbb, φ(b) = b
1116867a, b | aaba=1, bbababb=1⟩φ(a) = bbbb, φ(b) = b
1116869a, b | aaba=1, bbabbab=1⟩φ(a) = bbbb, φ(b) = b
1116870a, b | aaba=1, bbabbba=1⟩φ(a) = bbbb, φ(b) = b
1116875a, b | aaba=1, bbbaabb=1⟩φ(a) = bbbb, φ(b) = b
1116877a, b | aaba=1, bbbabab=1⟩φ(a) = bbbb, φ(b) = b
1116878a, b | aaba=1, bbbabba=1⟩φ(a) = bbbb, φ(b) = b
1116881a, b | aaba=1, bbbbaab=1⟩φ(a) = bbbb, φ(b) = b
1116882a, b | aaba=1, bbbbaba=1⟩φ(a) = bbbb, φ(b) = b
1116884a, b | aaba=1, bbbbbaa=1⟩φ(a) = bbbb, φ(b) = b
1117748a, b | aaab=1, abbbb=aaφ(a) = bbbb, φ(b) = b
1117780a, b | aaab=1, babbb=aaφ(a) = bbbb, φ(b) = b
1117796a, b | aaab=1, bbabb=aaφ(a) = bbbb, φ(b) = b
1117804a, b | aaab=1, bbbab=aaφ(a) = bbbb, φ(b) = b
1117808a, b | aaab=1, bbbba=aaφ(a) = bbbb, φ(b) = b
1117813a, b | aaab=1, bbbbb=abφ(a) = bbbb, φ(b) = b
1117814a, b | aaab=1, bbbbb=baφ(a) = bbbb, φ(b) = b
1117876a, b | aaba=1, abbbb=aaφ(a) = bbbb, φ(b) = b
1117908a, b | aaba=1, babbb=aaφ(a) = bbbb, φ(b) = b
1117924a, b | aaba=1, bbabb=aaφ(a) = bbbb, φ(b) = b
1117932a, b | aaba=1, bbbab=aaφ(a) = bbbb, φ(b) = b
1117936a, b | aaba=1, bbbba=aaφ(a) = bbbb, φ(b) = b
1117941a, b | aaba=1, bbbbb=abφ(a) = bbbb, φ(b) = b
1117942a, b | aaba=1, bbbbb=baφ(a) = bbbb, φ(b) = b
1118223a, b | aaa=b, aaaabbb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118227a, b | aaa=b, aaababb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118229a, b | aaa=b, aaabbab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118230a, b | aaa=b, aaabbba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118234a, b | aaa=b, aabaabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118236a, b | aaa=b, aababab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118237a, b | aaa=b, aababba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118239a, b | aaa=b, aabbaab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118240a, b | aaa=b, aabbaba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118242a, b | aaa=b, aabbbaa=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118248a, b | aaa=b, abaaabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118249a, b | aaa=b, abaabab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118250a, b | aaa=b, abaabba=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118252a, b | aaa=b, ababaab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118253a, b | aaa=b, abababa=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118258a, b | aaa=b, abbaaab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118269a, b | aaa=b, baaaabb=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118270a, b | aaa=b, baaabab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1118272a, b | aaa=b, baabaab=1⟩φ(a) = bbbbbbbbb, φ(b) = b
1121383a, b | aab=1, abbbbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121447a, b | aab=1, babbbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121479a, b | aab=1, bbabbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121495a, b | aab=1, bbbabbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121503a, b | aab=1, bbbbabbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121507a, b | aab=1, bbbbbabb=1⟩φ(a) = bbbbbb, φ(b) = b
1121509a, b | aab=1, bbbbbbab=1⟩φ(a) = bbbbbb, φ(b) = b
1121510a, b | aab=1, bbbbbbba=1⟩φ(a) = bbbbbb, φ(b) = b
1121611a, b | aba=1, abbbbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121637a, b | aba=1, babbbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121644a, b | aba=1, bbabbbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1121646a, b | aba=1, bbbabbbb=1⟩φ(a) = bbbbbb, φ(b) = b
1123112a, b | aab=1, bbbbb=aaaφ(a) = bbbbbb, φ(b) = b
1123258a, b | aba=1, bbbbb=aaaφ(a) = bbbbbb, φ(b) = b
1123682a, b | aa=b, aaabbbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123696a, b | aa=b, aababbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123702a, b | aa=b, aabbabbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123705a, b | aa=b, aabbbabb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123707a, b | aa=b, aabbbbab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123708a, b | aa=b, aabbbbba=1⟩φ(a) = bbbbbbb, φ(b) = b
1123721a, b | aa=b, abaabbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123726a, b | aa=b, abababbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123729a, b | aa=b, ababbabb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123730a, b | aa=b, ababbbab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123731a, b | aa=b, ababbbba=1⟩φ(a) = bbbbbbb, φ(b) = b
1123737a, b | aa=b, abbaabbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123739a, b | aa=b, abbababb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123740a, b | aa=b, abbabbab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123741a, b | aa=b, abbabbba=1⟩φ(a) = bbbbbbb, φ(b) = b
1123744a, b | aa=b, abbbaabb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123745a, b | aa=b, abbbabab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123747a, b | aa=b, abbbbaab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123759a, b | aa=b, baaabbbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123762a, b | aa=b, baababbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123764a, b | aa=b, baabbabb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123765a, b | aa=b, baabbbab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123769a, b | aa=b, babaabbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123770a, b | aa=b, babababb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123771a, b | aa=b, bababbab=1⟩φ(a) = bbbbbbb, φ(b) = b
1123773a, b | aa=b, babbaabb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123779a, b | aa=b, bbaaabbb=1⟩φ(a) = bbbbbbb, φ(b) = b
1123780a, b | aa=b, bbaababb=1⟩φ(a) = bbbbbbb, φ(b) = b