#23327 ⟨
a
,
b
|
aaa
=1,
bbbb
=
abbb
⟩
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Monoids with two generators and two relations
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#23326
⟨
a
,
b
|
aaa
=1,
bbbb
=
abba
⟩
Next:
#23328
⟨
a
,
b
|
aaa
=1,
bbbb
=
baab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
⇒ 1
[1]
2.
a
b
3
⇒
b
4
[2]
3.
b
6
⇒
b
3
[3]
# ab:aaa=1,bbbb=abbb ba aaa=1 abbb=bbbb bbbbbb=bbb