#2025 ⟨
a
,
b
|
abaaaaba
=
bb
⟩
Up:
Monoid enumeration
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#2024
⟨
a
,
b
|
abaaaaba
=
ab
⟩
Next:
#2026
⟨
a
,
b
|
abaaabab
=
aa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaabab
-1
b
-1
ab
⟩
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.
b
2
a
3
ba
⇒
ab
a
3
b
2
[2]
2.
ab
a
4
ba
⇒
b
2
[1]
3.
b
3
a
4
ba
⇒
ab
a
4
b
3
[3]
# ab:abaaaaba=bb ab - - bbaaaba=abaaabb abaaaaba=bb bbbaaaaba=abaaaabbb