#28197 ⟨a, b | aa=1, abbab=bbbb⟩
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 ⋅ b10 = b6 and b ⋅ b5 = b6, however b10 ≠ b5
- Not right cancellative, because right multiplication by b is not injective:
-
b2a ⋅ b = ab4 and ab3 ⋅ b = ab4, however b2a ≠ ab3
- 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,abbab=bbbb b/a - -
bbbbbbbbbbb=bbbbbb
babbbbbb=abbbbbbbbbb
bbab=abbbb
aa=1
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 28221 | ⟨a, b | aa=1, abbbb=bbab⟩ | φ(a) = a, φ(b) = b |