#10020 ⟨a, b | aa=1, abbbab=bb⟩
Contents
- Properties
- Rewriting system
- Anti-isomorphic instances
- Sum of relation sides is 10
- Infinite non-cancellative non-commutative monoid
- Element ba has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ b9 = b2 and b ⋅ b = b2, however b9 ≠ b
- Not right cancellative, because right multiplication by b is not injective:
-
ab ⋅ b = b3ab and b3a ⋅ b = b3ab, however ab ≠ b3a
- 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,abbbab=bb reversed:b/a - -
bbbbbbbbbb=bb
abb=bbbab
aa=1
bbabab=bbbbbb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 10 | 10330 | ⟨a, b | aa=1, babbb=bba⟩ | φ(a) = a, φ(b) = b |