#5921 ⟨
a
,
b
|
abbaab
=
baaaa
⟩
Up:
Monoid enumeration
Prev:
#5920
⟨
a
,
b
|
abbaab
=
abbba
⟩
Next:
#5922
⟨
a
,
b
|
abbaab
=
baaba
⟩
Contents
Properties
Rewriting system
Other submonoids of same group
Properties
Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaabbaaba
-1
b
-1
⟩
Anti-isomorphic embedding:
φ
(
a
) =
a
-1
,
φ
(
b
) =
baa
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
4
⇒
a
b
2
a
2
b
[1]
# ab:abbaab=baaaa b/a - - baaaa=abbaab
Other submonoids of same group
1 unique, 1 total
Σ
#
Presentation
Properties
11
3933
⟨
a
,
b
|
aaaabbaab
=
ba
⟩
Can
Inf