#27141 ⟨a, b | aa=1, abbabab=bb⟩
Contents
- Properties
- Rewriting system
- Anti-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 ⋅ b6 = b3 and b ⋅ b2 = b3, however b6 ≠ b2
- Not right cancellative, because right multiplication by b is not injective:
-
b(ba)2 ⋅ b = ab2 and ab ⋅ b = ab2, however b(ba)2 ≠ ab
- 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,abbabab=bb b/a - -
bbbbbbb=bbb
babbbbbb=babb
bbbbabb=abbbbbb
aa=1
ababb=bbabbb
abbabb=babbbbb
abbbabb=bbbabbbb
bbabab=abb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 27732 | ⟨a, b | aa=1, bababb=bba⟩ | φ(a) = a, φ(b) = b |