#1451 ⟨a, b | aabbababba=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 = da2
- b-1 = bcb(ba)2
- c-1 = d
- d-1 = c
- Reduced group presentation: ⟨a, b | aaabab-1b-1ab⟩
- Isomorphism: φ(a) = b-1, φ(b) = ba
- Auxiliary generators:
- c = aaa
- d = bbababb
- Reduction order:
- Left-to-right 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:aabbababba=1 cda/b aaa=c,bbababb=d magic:0
cd=1
dc=1
ac=ca
ad=da
aaa=c
abbcb=bcbba
ababb=cbbabda
aabbab=babbaa
aabcbb=cbbcbdaa
cbbabab=bcbbaba
dbcbbab=bbababdaa
cabbabab=abcbbaba
dabcbbab=abbababdaa
bbcbbab=daa
aabbbcbb=babbaabcbdaa
cbbabcbbab=bcbbabaabbaa
dbcbbbcbb=bbababdaabcbdaa
cabbabcbbab=abcbbabaabbaa
dabcbbbcbb=abbababdaabcbdaa
bbcbbbcbb=daabcbdaa
cbbabcbbbcbb=bcbbabaabbaabcbdaa
cabbabcbbbcbb=abcbbabaabbaabcbdaa
2 unique, 2 total
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
4 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1452 | ⟨a, b | aabbabbaab=1⟩ | φ(a) = bcbbabadaaa, φ(b) = daaabab |
| 10 | 1501 | ⟨a, b | abaabbabba=1⟩ | φ(a) = bcbbabadaaa, φ(b) = abdaaab |
| 10 | 1502 | ⟨a, b | abaabbbaab=1⟩ | φ(a) = daaab, φ(b) = a |
| 10 | 1510 | ⟨a, b | ababaabbba=1⟩ | φ(a) = daaab, φ(b) = a |