#1607 ⟨a, b | aaa=bb, bab=b⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 9
- Infinite non-cancellative non-commutative monoid
- Element ba2 has infinite order
- Not left cancellative, because left multiplication by b is not injective:
-
b ⋅ ab = b and b ⋅ 1 = b, however ab ≠ 1
- Not right cancellative, because right multiplication by b is not injective:
-
ba ⋅ b = b and 1 ⋅ b = b, however ba ≠ 1
- 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:aaa=bb,bab=b b/a - -
bbbbbbb=bb
abb=bbbbbb
bab=b
bba=bbbbbb
aaa=bb
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 20197 | ⟨a, b | aba=a, aaba=bbb⟩ | φ(a) = b, φ(b) = a |