#25239 ⟨
a
,
b
|
aa
=
a
,
babab
=
bbb
⟩
Up:
Monoid enumeration
Prev:
#25238
⟨
a
,
b
|
aa
=
a
,
babab
=
bab
⟩
Next:
#25242
⟨
a
,
b
|
aa
=
a
,
babbb
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
b
2
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
=
a
and
a
⋅ 1 =
a
, however
a
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
a
⋅
a
=
a
and 1 ⋅
a
=
a
, however
a
≠ 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
2
⇒
a
[1]
2.
b
(
ab
)
2
⇒
b
3
[2]
3.
b
3
ab
⇒
ba
b
3
[3]
# ab:aa=a,babab=bbb ab - - aa=a babab=bbb bbbab=babbb