#5722 ⟨
a
,
b
|
aaaa
=1,
baaab
=
a
⟩
Up:
Monoid enumeration
Prev:
#5717
⟨
a
,
b
|
aaaa
=1,
abbab
=
b
⟩
Next:
#5723
⟨
a
,
b
|
aaaa
=1,
baaab
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-Abelian group
Element
a
2
b
has infinite order
Inverses of generators:
a
-1
=
a
3
b
-1
=
a
3
b
a
3
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
a
3
b
⇒
a
[2]
# ab:aaaa=1,baaab=a ab - - aaaa=1 baaab=a