#5306 ⟨
a
,
b
|
abaaaba
=
bbbb
⟩
Up:
Monoid enumeration
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#5305
⟨
a
,
b
|
abaaaba
=
babb
⟩
Next:
#5307
⟨
a
,
b
|
abaabab
=
aaaa
⟩
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
|
aaaaba
-1
bbba
-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.
ab
a
3
ba
⇒
b
4
[1]
2.
b
4
a
2
ba
⇒
ab
a
2
b
4
[2]
3.
b
5
a
3
ba
⇒
ab
a
3
b
5
[3]
# ab:abaaaba=bbbb ab - - abaaaba=bbbb bbbbaaba=abaabbbb bbbbbaaaba=abaaabbbbb