#2274 ⟨
a
,
b
|
aabbbaa
=
bbb
⟩
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Monoid enumeration
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#2273
⟨
a
,
b
|
aabbbaa
=
bab
⟩
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#2275
⟨
a
,
b
|
aabbbab
=
aaa
⟩
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
|
aaabba
-1
a
-1
a
-1
bb
⟩
Embedding:
φ
(
a
) =
b
,
φ
(
b
) =
a
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
2
b
3
a
2
⇒
b
3
[1]
2.
b
6
a
2
⇒
a
2
b
6
[2]
3.
(
b
3
a
)
2
a
⇒
a
(
a
b
3
)
2
[3]
# ab:aabbbaa=bbb ab - - aabbbaa=bbb bbbbbbaa=aabbbbbb bbbabbbaa=aabbbabbb