#1255 ⟨
a
,
b
|
ababa
=
aaaa
⟩
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Monoid enumeration
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#1254
⟨
a
,
b
|
abaab
=
bbbb
⟩
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#1256
⟨
a
,
b
|
ababa
=
aaab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ba
)
2
=
a
4
and
a
⋅
a
3
=
a
4
, however (
ba
)
2
≠
a
3
Not right cancellative, because right multiplication by
a
is not injective:
(
ab
)
2
⋅
a
=
a
4
and
a
3
⋅
a
=
a
4
, however (
ab
)
2
≠
a
3
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
(
ba
)
2
⇒
a
4
[1]
2.
ab
a
4
⇒
a
4
ba
[2]
# ab:ababa=aaaa ab - - ababa=aaaa abaaaa=aaaaba