#1709 ⟨a, b | aabbaaaab=a⟩
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- Properties
- Rewriting system
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ ab2a4b = a and a ⋅ 1 = a, however ab2a4b ≠ 1
- Enveloping group: ⟨a, b | aaabba-1b⟩
- Auxiliary generators:
- c = aaaa
- Reduction order:
- Left-to-right recursive path with deg(b) = deg(c) = 0, b < c; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
- Morphocompletion: how the auxiliary generators were found.
| # | Rule | Proof |
|---|
| 1. |
c2b2cb ⇒ cb(bc)2 |
[9] |
| 2. |
c2(bcb)2 ⇒ c2b3cbc |
[20] |
| 3. |
(cb)3bcb ⇒ cbcb3cbc |
[19] |
| 4. |
(cb2cb)2 ⇒ c(b2cb)2c |
[11] |
| 5. |
c2b3c(bcb)2 ⇒ c2(b3c)2bc |
[22] |
| 6. |
cbcb3c(bcb)2 ⇒ cbc(b3c)2bc |
[21] |
| 7. |
cb2cb3c(bcb)2 ⇒ c(b2cb)3c |
[17] |
| 8. |
c2(b3c)2(bcb)2 ⇒ cbc(b3c)2bcb2c |
[23] |
| 9. |
cbc(b3c)2(bcb)2 ⇒ c(b2cb)3cb2c |
[18] |
| 10. |
c(b2cb)3cb2cb ⇒ c |
[16] |
| 11. |
a ⇒ c(b2cb)3 |
[14] |
# ab:aabbaaaab=a bc/a aaaa=c morph:4/0
ccbbcb=cbbcbc
ccbcbbcb=ccbbbcbc
cbcbcbbcb=cbcbbbcbc
cbbcbcbbcb=cbbcbbbcbc
ccbbbcbcbbcb=ccbbbcbbbcbc
cbcbbbcbcbbcb=cbcbbbcbbbcbc
cbbcbbbcbcbbcb=cbbcbbbcbbbcbc
ccbbbcbbbcbcbbcb=cbcbbbcbbbcbcbbc
cbcbbbcbbbcbcbbcb=cbbcbbbcbbbcbcbbc
cbbcbbbcbbbcbcbbcb=c
a=cbbcbbbcbbbcb