#7279 ⟨
a
,
b
|
aaa
=1,
bbbbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#7249
⟨
a
,
b
|
aaa
=1,
ababbbb
=1⟩
Next:
#7519
⟨
a
,
b
|
aaa
=1,
ababba
=
b
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Isomorphic to ℤ
3
∗ ℤ
7
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
2
b
-1
=
b
6
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
3
⇒ 1
[1]
2.
b
7
⇒ 1
[2]
# ab:aaa=1,bbbbbbb=1 ab aaa=1 bbbbbbb=1