#99 ⟨
a
,
b
|
aaab
=
ba
⟩
Up:
Monoid enumeration
Prev:
#98
⟨
a
,
b
|
aaab
=
ab
⟩
Next:
#100
⟨
a
,
b
|
aaab
=
bb
⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 6
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaba
-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
3
b
⇒
ba
[1]
# ab:aaab=ba ab - - aaab=ba
Other submonoids of same group
2 unique, 2 total
Σ
#
Presentation
Properties
8
474
⟨
a
,
b
|
ababab
=
ba
⟩
Can
Inf
10
2036
⟨
a
,
b
|
abaabaab
=
ba
⟩
Can
Inf