#346 ⟨
a
,
b
|
aaaaaba
=
b
⟩
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Monoid enumeration
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#345
⟨
a
,
b
|
aaaaaba
=
a
⟩
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#347
⟨
a
,
b
|
aaaaabb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaaabab
-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
5
b
2
⇒
b
a
4
ba
[2]
2.
a
5
ba
⇒
b
[1]
# ab:aaaaaba=b ba - - aaaaabb=baaaaba aaaaaba=b