#3776 ⟨
a
,
b
|
aaaa
=
bb
,
bbbb
=1⟩
Up:
Monoid enumeration
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#3773
⟨
a
,
b
|
aaaa
=
bb
,
abbb
=1⟩
Next:
#3780
⟨
a
,
b
|
aaab
=
aa
,
abab
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-Abelian group
Element
a
2
ba
has infinite order
Inverses of generators:
a
-1
=
a
3
b
2
b
-1
=
b
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.
b
2
a
⇒
a
b
2
[3]
2.
a
4
⇒
b
2
[1]
3.
b
4
⇒ 1
[2]
# ab:aaaa=bb,bbbb=1 ab - - bba=abb aaaa=bb bbbb=1