#21786 ⟨
a
,
b
|
aaa
=1,
bbabbbb
=
a
⟩
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Monoid enumeration
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#21783
⟨
a
,
b
|
aaa
=1,
bbaabbb
=
b
⟩
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#21787
⟨
a
,
b
|
aaa
=1,
bbabbbb
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-Abelian group
Element
aba
has infinite order
Inverses of generators:
a
-1
=
a
2
b
-1
=
b
17
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:
Right-to-left recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
18
⇒ 1
[14]
2.
a
b
2
⇒
b
8
a
[13]
3.
a
3
⇒ 1
[1]
# ab:aaa=1,bbabbbb=a reversed:b/a - - bbbbbbbbbbbbbbbbbb=1 abb=bbbbbbbba aaa=1