#5753 ⟨
a
,
b
|
aaab
=1,
abaab
=
b
⟩
Up:
Monoid enumeration
Prev:
#5745
⟨
a
,
b
|
aaab
=1,
aabab
=
b
⟩
Next:
#5868
⟨
a
,
b
|
aabb
=1,
aaabb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
2
ba
=
a
and
a
⋅ 1 =
a
, however
a
2
ba
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
ba
⋅
b
=
a
b
2
and
ab
⋅
b
=
a
b
2
, however
ba
≠
ab
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.
bab
⇒
a
b
2
[4]
2.
a
3
b
⇒ 1
[1]
3.
b
a
2
b
⇒
a
2
b
2
[5]
# ab:aaab=1,abaab=b ab - - bab=abb aaab=1 baab=aabb