#1408 ⟨a, b | aabaababba=1⟩
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- Properties
- Rewriting system
- Other submonoids of same group
- Isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-Abelian group
- Inverses of generators:
- a-1 = a2d
- b-1 = cba(ab)2
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aababbab-1⟩
- Isomorphism: φ(a) = b-1, φ(b) = bab
- Auxiliary generators:
- c = aaa
- d = baababb
- Reduction order:
- Right-to-left recursive path with deg(c) = deg(d) = deg(a) = 0, c < d < a; deg(b) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aabaababba=1 reversed:cda/b aaa=c,baababb=d magic:0
dc=1
cd=1
ca=ac
da=ad
aaa=c
babbc=abaabab
baababd=aadbabb
babba=aadbbcb
bbcba=aadbcbaab
baababa=adbbcbc
bcbaaba=cbaabab
baababb=d
bbcbbbc=abababaabab
bcbaabbbc=abbacbaabab
bbcbcbbc=aabaabaabaabab
bcbaabbabd=aababaadbabb
bbcbcbabd=aadbcbababb
bcbaabcbabd=cbaabbabb
bbcbbba=ababaadbbcb
bcbaabbba=abbaabbcb
bbcbcbba=aabaabbbcb
bcbaabbaba=aababadbbcbc
bbcbcbaba=aadbcbbbcbc
bcbaabcbaba=cbaabaadbbcbc
bcbaabbabb=aababd
bbcbcbabb=aadbcbaad
bcbaabcbabb=cbaabad
4 unique, 4 total
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
5 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1426 | ⟨a, b | aababbaaab=1⟩ | φ(a) = a, φ(b) = aadaadaba |
| 10 | 1448 | ⟨a, b | aabbabaaba=1⟩ | φ(a) = aad, φ(b) = aaba |
| 10 | 1488 | ⟨a, b | abaaabbaba=1⟩ | φ(a) = aad, φ(b) = aaba |
| 10 | 1521 | ⟨a, b | ababbabbba=1⟩ | φ(a) = aaba, φ(b) = aad |
| 10 | 1529 | ⟨a, b | abbaaabaab=1⟩ | φ(a) = a, φ(b) = aadaadaba |