#27125 ⟨a, b | aa=1, ababbba=bb⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b5 = b2 and b ⋅ b = b2, however b5 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
b5 ⋅ b = b2 and b ⋅ b = b2, however b5 ≠ b
- Reduction order:
- Left-to-right recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,ababbba=bb b/a - -
bbbbbb=bb
bbabbbb=bba
bbbba=abbbb
aa=1
ababb=bbabbb
abba=babbb
abbba=bbbabb
bbaba=abbbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
2 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 27656 | ⟨a, b | aa=1, ababbb=bba⟩ | φ(a) = a, φ(b) = b |
| 11 | 28266 | ⟨a, b | aa=1, babbb=abba⟩ | φ(a) = a, φ(b) = b |