#5726 ⟨
a
,
b
|
aaaa
=1,
babab
=
a
⟩
Up:
Monoid enumeration
Prev:
#5725
⟨
a
,
b
|
aaaa
=1,
baabb
=
b
⟩
Next:
#5727
⟨
a
,
b
|
aaaa
=1,
babab
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-Abelian group
Element
a
b
2
has infinite order
Inverses of generators:
a
-1
=
a
3
b
-1
=
a
3
(
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.
b
a
2
⇒
a
2
b
[3]
2.
a
4
⇒ 1
[1]
3.
b
(
ab
)
2
⇒
a
[2]
# ab:aaaa=1,babab=a ab - - baa=aab aaaa=1 babab=a