#44 ⟨
a
,
b
|
aaa
=
aa
⟩
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Monoids with two generators and one relation
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#43
⟨
a
,
b
|
abba
=
b
⟩
Next:
#45
⟨
a
,
b
|
aaa
=
ab
⟩
Properties
Presentation has sum-of-sides 5
Isomorphic to ℕ
(3 = 2)
∗ ℕ
Infinite non-commutative monoid
Complete 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
a
3
⇒
a
2
# ab:aaa=aa ab aaa=aa
Right Cayley graph (truncated)
Left Cayley graph (truncated)
