#23311 ⟨
a
,
b
|
aaa
=1,
babb
=
abbb
⟩
Up:
Monoid enumeration
Prev:
#23310
⟨
a
,
b
|
aaa
=1,
babb
=
abba
⟩
Next:
#23313
⟨
a
,
b
|
aaa
=1,
babb
=
baab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
aba
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
bab
⋅
b
=
a
b
3
and
a
b
2
⋅
b
=
a
b
3
, however
bab
≠
a
b
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
3
⇒ 1
[1]
2.
ba
b
2
⇒
a
b
3
[2]
3.
b
a
2
b
4
⇒
a
2
b
5
[3]
# ab:aaa=1,babb=abbb ab - - aaa=1 babb=abbb baabbbb=aabbbbb