#17645 ⟨
a
,
b
|
aaaa
=1,
aabbb
=
bb
⟩
Up:
Monoid enumeration
Prev:
#17637
⟨
a
,
b
|
aaaa
=1,
aabab
=
bb
⟩
Next:
#17647
⟨
a
,
b
|
aaaa
=1,
abaab
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
2
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
3
=
b
2
and
b
⋅
b
=
b
2
, however
b
3
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
b
3
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
b
3
≠
b
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.
a
2
b
2
⇒
b
3
[3]
3.
b
4
⇒
b
2
[4]
# ab:aaaa=1,aabbb=bb ab - - aaaa=1 aabb=bbb bbbb=bb