#801 ⟨
a
,
b
|
aababaab
=
a
⟩
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Monoids with two generators and one relation
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#800
⟨
a
,
b
|
aabaabba
=
b
⟩
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#802
⟨
a
,
b
|
aababaab
=
b
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ab
)
2
a
2
b
=
a
and
a
⋅ 1 =
a
, however (
ab
)
2
a
2
b
≠ 1
Enveloping group is isomorphic to ℤ
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
2
ba
⇒
a
3
b
[4]
2.
a
3
b
2
a
⇒
a
4
b
2
[6]
3.
a
5
b
3
⇒
a
[7]
# ab:aababaab=a ab aaba=aaab aaabba=aaaabb aaaaabbb=a