#4604 ⟨
a
,
b
|
aabaaaba
=
bbb
⟩
Up:
Monoid enumeration
Prev:
#4603
⟨
a
,
b
|
aabaaaba
=
bba
⟩
Next:
#4605
⟨
a
,
b
|
aabaaabb
=
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
|
aaabaab
-1
b
-1
b
-1
ab
⟩
Anti-isomorphic 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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
3
⇒ (
a
2
ba
)
2
[1]
2.
(
a
2
ba
)
2
b
⇒
b
(
a
2
ba
)
2
[2]
# ab:aabaaaba=bbb a/b - - bbb=aabaaaba aabaaabab=baabaaaba