#27160 ⟨a, b | aa=1, abbbbab=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 ⋅ b(ab)2 = b7 and b ⋅ b6 = b7, however b(ab)2 ≠ b6
- Not right cancellative, because right multiplication by b is not injective:
-
ab ⋅ b = b4ab and b4a ⋅ b = b4ab, however ab ≠ b4a
- Reduction order:
- Right-to-left recursive path with deg(b) = 0; deg(a) = 1
- Certificate: derivations of all rewriting rules from the defining relations.
# ab:aa=1,abbbbab=bb reversed:b/a - -
bbbbbbbbbbbbbbbbb=bb
abb=bbbbab
aa=1
bbabab=bbbbbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 27746 | ⟨a, b | aa=1, babbbb=bba⟩ | φ(a) = a, φ(b) = b |