#5556 ⟨
a
,
b
|
aaabaa
=
babbb
⟩
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Monoid enumeration
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#5555
⟨
a
,
b
|
aaabaa
=
babba
⟩
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#5557
⟨
a
,
b
|
aaabaa
=
bbaaa
⟩
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
a
-1
b
-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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
b
3
⇒
a
3
b
a
2
[1]
2.
a
3
b
a
3
b
3
⇒
ba
b
2
a
3
b
a
2
[2]
# ab:aaabaa=babbb a/b - - babbb=aaabaa aaabaaabbb=babbaaabaa