#4419 ⟨
a
,
b
|
aaaaabbb
=
baa
⟩
Up:
Monoid enumeration
Prev:
#4418
⟨
a
,
b
|
aaaaabbb
=
abb
⟩
Next:
#4420
⟨
a
,
b
|
aaaaabbb
=
bab
⟩
Contents
Properties
Rewriting system
Other submonoids of anti-isomorphic group
Properties
Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaaabbba
-1
a
-1
b
-1
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
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
5
b
3
⇒
b
a
2
[1]
# ab:aaaaabbb=baa ab - - aaaaabbb=baa
Other submonoids of anti-isomorphic group
1 unique, 1 total
Σ
#
Presentation
Properties
11
5465
⟨
a
,
b
|
aaaaab
=
bbbaa
⟩
Can
Inf