#13765 ⟨
a
,
b
|
abbba
=1,
aaaaaa
=1⟩
Up:
Monoids with two generators and two relations
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#13552
⟨
a
,
b
|
aabab
=1,
aabbbb
=1⟩
Next:
#13836
⟨
a
,
b
|
aaaa
=
a
,
bbbbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
5
b
-1
=
b
2
a
2
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
6
⇒ 1
[2]
2.
a
2
b
⇒
b
a
2
[9]
3.
b
3
⇒
a
4
[6]
# ab:abbba=1,aaaaaa=1 a/b aaaaaa=1 aab=baa bbb=aaaa