#27671 ⟨a, b | aa=1, abbabb=bab⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ab5 = bab and b ⋅ ab = bab, however ab5 ≠ ab
- Not right cancellative, because right multiplication by b is not injective:
-
bab4 ⋅ b = bab and ba ⋅ b = bab, however bab4 ≠ ba
- 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,abbabb=bab b/a - -
babbbbb=bab
bbbbbab=bab
aa=1
abab=bbabb
abbab=babbbb
abbbab=bbbabbb
babbbbab=abbbbabb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 28280 | ⟨a, b | aa=1, bbabb=abab⟩ | φ(a) = a, φ(b) = b |