#13552 ⟨
a
,
b
|
aabab
=1,
aabbbb
=1⟩
Up:
Monoid enumeration
Prev:
#13550
⟨
a
,
b
|
aabab
=1,
aabbab
=1⟩
Next:
#13836
⟨
a
,
b
|
aaaa
=
a
,
bbbbbb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
(
ba
)
2
=
a
and
a
⋅ 1 =
a
, however
a
(
ba
)
2
≠ 1
Not right cancellative, because right multiplication by (
ab
)
2
is not injective:
a
(
ba
)
2
⋅ (
ab
)
2
= (
ab
)
2
and 1 ⋅ (
ab
)
2
= (
ab
)
2
, however
a
(
ba
)
2
≠ 1
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
(
ab
)
2
⇒ 1
[1]
2.
a
2
b
4
⇒ 1
[2]
# ab:aabab=1,aabbbb=1 ab - - aabab=1 aabbbb=1