#4011 ⟨
a
,
b
|
aab
=
aaa
,
bbbb
=1⟩
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Monoids with two generators and two relations
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#3991
⟨
a
,
b
|
baba
=
ba
,
bbaa
=1⟩
Next:
#4021
⟨
a
,
b
|
aba
=
aaa
,
bbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
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
2
b
⇒
a
3
[1]
2.
b
4
⇒ 1
[2]
3.
a
6
⇒
a
2
[3]
# ab:aab=aaa,bbbb=1 ab aab=aaa bbbb=1 aaaaaa=aa