#11639 ⟨
a
,
b
|
aaaa
=
aa
,
bbbbb
=1⟩
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Monoids with two generators and two relations
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#11609
⟨
a
,
b
|
babaa
=
b
,
bbaaa
=1⟩
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#11723
⟨
a
,
b
|
aaab
=
aa
,
bbbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Isomorphic to ℕ
(4 = 2)
∗ ℤ
5
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
4
⇒
a
2
[1]
2.
b
5
⇒ 1
[2]
# ab:aaaa=aa,bbbbb=1 ab aaaa=aa bbbbb=1