#414 ⟨
a
,
b
|
aaaaaa
=
ab
⟩
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Monoids with two generators and one relation
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#413
⟨
a
,
b
|
aaaaaa
=
aa
⟩
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#415
⟨
a
,
b
|
aaaaaa
=
bb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 8
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
5
=
ab
and
a
⋅
b
=
ab
, however
a
5
≠
b
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
a
6
[1]
# ab:aaaaaa=ab a/b ab=aaaaaa