#11343 ⟨
a
,
b
|
aabaa
=
b
,
bbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#11325
⟨
a
,
b
|
aabaa
=
a
,
bbbbb
=1⟩
Next:
#11345
⟨
a
,
b
|
aabab
=
a
,
aabbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
3
b
-1
=
b
4
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
a
2
⇒
a
2
b
[4]
2.
a
4
⇒ 1
[6]
3.
b
5
⇒ 1
[2]
# ab:aabaa=b,bbbbb=1 ab baa=aab aaaa=1 bbbbb=1