#15778 ⟨
a
,
b
|
aab
=
bb
,
babaa
=
b
⟩
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Monoid enumeration
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#15770
⟨
a
,
b
|
aab
=
bb
,
baaaa
=
b
⟩
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#15780
⟨
a
,
b
|
aab
=
bb
,
babab
=
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
⋅
ab
a
2
=
b
and
b
⋅ 1 =
b
, however
ab
a
2
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
2
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
a
2
≠
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
2
b
⇒
b
2
[1]
2.
bab
a
2
⇒
b
[2]
3.
ba
b
3
⇒
b
2
[3]
4.
(
ba
)
2
b
2
⇒
bab
[4]
# ab:aab=bb,babaa=b ab - - aab=bb babaa=b babbb=bb bababb=bab