#108 ⟨
a
,
b
|
abab
=
aa
⟩
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Monoids with two generators and one relation
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#107
⟨
a
,
b
|
aabb
=
ba
⟩
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#109
⟨
a
,
b
|
abab
=
ab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 6
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
bab
=
a
2
and
a
⋅
a
=
a
2
, however
bab
≠
a
Enveloping group: ⟨
a
,
b
|
aabb
⟩
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
ab
)
2
⇒
a
2
[1]
2.
a
3
b
⇒
ab
a
2
[2]
# ab:abab=aa ba abab=aa aaab=abaa