#350 ⟨
a
,
b
|
aaaabaa
=
b
⟩
Up:
Monoid enumeration
Prev:
#349
⟨
a
,
b
|
aaaabaa
=
a
⟩
Next:
#351
⟨
a
,
b
|
aaaabab
=
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
|
aaaabaab
-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
4
b
2
⇒ (
b
a
2
)
2
[2]
2.
a
4
bab
⇒
b
a
3
b
a
2
[3]
3.
a
4
b
a
2
⇒
b
[1]
# ab:aaaabaa=b ba - - aaaabb=baabaa aaaabab=baaabaa aaaabaa=b