#166 ⟨
a
,
b
|
aaaaba
=
b
⟩
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Monoid enumeration
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#165
⟨
a
,
b
|
aaaaba
=
a
⟩
Next:
#167
⟨
a
,
b
|
aaaabb
=
a
⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 7
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaabab
-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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
b
2
⇒
b
a
3
ba
[2]
2.
a
4
ba
⇒
b
[1]
# ab:aaaaba=b ba - - aaaabb=baaaba aaaaba=b
Other submonoids of same group
1 unique, 3 total
Σ
#
Presentation
Properties
φ
10
1513
⟨
a
,
b
|
ababababba
=1⟩
Grp
Inf
2