#202 ⟨
a
,
b
|
aaaab
=
ba
⟩
Up:
Monoid enumeration
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#201
⟨
a
,
b
|
aaaab
=
ab
⟩
Next:
#203
⟨
a
,
b
|
aaaab
=
bb
⟩
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
|
aaaaba
-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
4
b
⇒
ba
[1]
# ab:aaaab=ba ab - - aaaab=ba
Other submonoids of same group
1 unique, 1 total
Σ
#
Presentation
Properties
10
2055
⟨
a
,
b
|
abababab
=
ba
⟩
Can
Inf