#1615 ⟨a, b | aaabaabaa=a⟩
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- Properties
- Rewriting system
- Anti-isomorphic instances
- Presentation has sum-of-sides 10
- Infinite non-cancellative non-commutative monoid
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a2(ba2)2 = a and a ⋅ 1 = a, however a2(ba2)2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a(a2b)2a ⋅ a = a and 1 ⋅ a = a, however a(a2b)2a ≠ 1
- Enveloping group: ⟨a, b | aabb⟩
- Auxiliary generators:
- c = aa
- Reduction order:
- Right-to-left 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.
# ab:aaabaabaa=a reversed:bc/a aa=c morph:2/0
cbcc=ccbc
ccbcbc=c
cbca=ccba
ccbcba=a
ac=ca
abcc=cabc
abcbc=cbcba
aa=c
abca=caba
abcba=cbcbcbcbc
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 1665 | ⟨a, b | aabaaaaba=a⟩ | φ(a) = a, φ(b) = b |