#3518 ⟨
a
,
b
|
aaabbbabba
=
b
⟩
Up:
Monoid enumeration
Prev:
#3517
⟨
a
,
b
|
aaabbbabba
=
a
⟩
Next:
#3520
⟨
a
,
b
|
aaabbbbaaa
=
b
⟩
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
|
aaabaaba
-1
bbb
⟩
Embedding:
φ
(
a
) =
b
,
φ
(
b
) =
a
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
2
(
a
b
3
)
2
⇒
b
a
2
b
(
b
2
a
)
2
[2]
2.
a
3
b
(
b
2
a
)
2
⇒
b
[1]
# ab:aaabbbabba=b ba - - aaabbbabbb=baabbbabba aaabbbabba=b