#4685 ⟨
a
,
b
|
aaab
=
b
,
abbb
=
a
⟩
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Monoids with two generators and two relations
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#4684
⟨
a
,
b
|
aaab
=
b
,
abba
=
b
⟩
Next:
#4686
⟨
a
,
b
|
aaab
=
b
,
baaa
=
b
⟩
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.
b
3
⇒
a
3
[3]
2.
a
4
⇒
a
[5]
3.
a
3
b
⇒
b
[1]
4.
b
a
3
⇒
b
[4]
# ab:aaab=b,abbb=a ab bbb=aaa aaaa=a aaab=b baaa=b