#4634 ⟨
a
,
b
|
aabaabba
=
bbb
⟩
Up:
Monoid enumeration
Prev:
#4633
⟨
a
,
b
|
aabaabba
=
bba
⟩
Next:
#4635
⟨
a
,
b
|
aababaab
=
aaa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaabba
-1
bba
-1
a
-1
b
⟩
Embedding:
φ
(
a
) =
b
,
φ
(
b
) =
a
-1
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
)
2
ba
⇒
b
3
[1]
2.
b
3
ab
a
2
b
2
a
⇒
a
2
b
a
2
b
5
[2]
# ab:aabaabba=bbb ab - - aabaabba=bbb bbbabaabba=aabaabbbbb