#14496 ⟨
a
,
b
|
aaab
=
b
,
ababb
=
b
⟩
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Monoid enumeration
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#14494
⟨
a
,
b
|
aaab
=
b
,
ababa
=
b
⟩
Next:
#14498
⟨
a
,
b
|
aaab
=
b
,
abbaa
=
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
)
2
=
b
and
b
⋅ 1 =
b
, however (
ab
)
2
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
a
3
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
3
≠ 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
3
b
⇒
b
[1]
2.
ba
b
2
⇒
a
2
b
[3]
3.
b
(
ab
)
2
⇒
b
[6]
4.
bab
a
2
b
⇒
ab
[5]
# ab:aaab=b,ababb=b ab - - aaab=b babb=aab babab=b babaab=ab