#19303 ⟨
a
,
b
|
aaa
=
a
,
bbbbb
=
bb
⟩
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Monoids with two generators and two relations
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#19302
⟨
a
,
b
|
aaa
=
a
,
bbbbb
=
ab
⟩
Next:
#19374
⟨
a
,
b
|
aaa
=
b
,
bbbbb
=
ab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Isomorphic to ℕ
(3 = 1)
∗ ℕ
(5 = 2)
Infinite non-commutative monoid
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
3
⇒
a
[1]
2.
b
5
⇒
b
2
[2]
# ab:aaa=a,bbbbb=bb ab aaa=a bbbbb=bb