#116 ⟨
a
,
b
|
aba
=
aab
⟩
Up:
Monoids with two generators and one relation
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#115
⟨
a
,
b
|
aba
=
aaa
⟩
Next:
#117
⟨
a
,
b
|
abb
=
aaa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 6
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ba
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
ba
≠
ab
Enveloping group: ⟨
a
,
b
|
aba
-1
b
-1
⟩
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
⇒
aba
[1]
# ab:aba=aab ba aab=aba