#5440 ⟨
a
,
b
|
aaaa
=1,
ababab
=1⟩
Up:
Monoid enumeration
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#5436
⟨
a
,
b
|
aaaa
=1,
aabbbb
=1⟩
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#5442
⟨
a
,
b
|
aaaa
=1,
ababbb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-Abelian group
Element
ab
a
2
has infinite order
Inverses of generators:
a
-1
=
a
3
b
-1
=
a
(
ba
)
2
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
⇒ 1
[1]
2.
b
(
ab
)
2
⇒
a
3
[3]
# ab:aaaa=1,ababab=1 ab - - aaaa=1 babab=aaa