#5841 ⟨
a
,
b
|
abaaba
=
aaaaa
⟩
Up:
Monoids with two generators and one relation
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#5840
⟨
a
,
b
|
abaaab
=
bbbbb
⟩
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#5842
⟨
a
,
b
|
abaaba
=
aaaab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
a
2
ba
=
a
5
and
a
⋅
a
4
=
a
5
, however
b
a
2
ba
≠
a
4
Not right cancellative, because right multiplication by
a
is not injective:
ab
a
2
b
⋅
a
=
a
5
and
a
4
⋅
a
=
a
5
, however
ab
a
2
b
≠
a
4
Enveloping group: ⟨
a
,
b
|
aaaaabb
⟩
Rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
1
1
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
aba
)
2
⇒
a
5
[1]
2.
ab
a
6
⇒
a
6
ba
[2]
# ab:abaaba=aaaaa ab abaaba=aaaaa abaaaaaa=aaaaaaba