#12264 ⟨a, b | aaab=ab, bbab=a⟩
Contents
- Properties
- Rewriting system
- Isomorphic instances
- Sum of relation sides is 11
- Infinite non-cancellative non-commutative monoid
- Element b has infinite order
- Not left cancellative, because left multiplication by a is not injective:
-
a ⋅ a2 = a and a ⋅ 1 = a, however a2 ≠ 1
- Not right cancellative, because right multiplication by a is not injective:
-
a2 ⋅ a = a and 1 ⋅ a = a, however a2 ≠ 1
- 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:aaab=ab,bbab=a reversed:b/a - -
bbbbbba=a
ab=bbbba
aaa=a
The mapping is from the listed presentation's alphabet to the current rewriting system's alphabet.
1 total
| Σ | # | Presentation | Mapping |
|---|
| 11 | 12372 | ⟨a, b | aaba=ab, bbab=a⟩ | φ(a) = a, φ(b) = b |