#12255 ⟨
a
,
b
|
aaab
=
ab
,
baaa
=
b
⟩
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Monoid enumeration
Prev:
#12241
⟨
a
,
b
|
aaab
=
aa
,
bbbb
=
b
⟩
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#12257
⟨
a
,
b
|
aaab
=
ab
,
baab
=
b
⟩
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
b
is not injective:
b
⋅
a
3
=
b
and
b
⋅ 1 =
b
, however
a
3
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
ba
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
ba
≠
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.
bab
⇒
b
2
[3]
2.
a
3
b
⇒
ab
[1]
3.
b
a
3
⇒
b
[2]
4.
b
a
2
b
⇒
b
2
[4]
# ab:aaab=ab,baaa=b ab - - bab=bb aaab=ab baaa=b baab=bb