#1061 ⟨
a
,
b
|
aabaab
=
aaa
⟩
Up:
Monoids with two generators and one relation
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#1060
⟨
a
,
b
|
aaabbb
=
baa
⟩
Next:
#1062
⟨
a
,
b
|
aabaab
=
aab
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 9
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ab
a
2
b
=
a
3
and
a
⋅
a
2
=
a
3
, however
ab
a
2
b
≠
a
2
Enveloping group: ⟨
a
,
b
|
aaabb
⟩
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
a
2
b
)
2
⇒
a
3
[1]
2.
a
5
b
⇒
a
2
b
a
3
[2]
# ab:aabaab=aaa ba aabaab=aaa aaaaab=aabaaa