#595 ⟨
a
,
b
|
aaaaaaaaa
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#594
⟨
a
,
b
|
bbbb
=
aaaa
⟩
Next:
#596
⟨
a
,
b
|
aaaaaaaab
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 9
Isomorphic to ℤ
9
∗ ℕ
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aaaaaaaaa
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
Rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
9
⇒ 1
[1]
# ab:aaaaaaaaa=1 ab aaaaaaaaa=1