#1151 ⟨
a
,
b
|
aaaab
=
aaba
⟩
Up:
Monoids with two generators and one relation
Prev:
#1150
⟨
a
,
b
|
aaaab
=
aaab
⟩
Next:
#1152
⟨
a
,
b
|
aaaab
=
aabb
⟩
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
⋅
a
3
b
=
a
2
ba
and
a
⋅
aba
=
a
2
ba
, however
a
3
b
≠
aba
Enveloping group: ⟨
a
,
b
|
aaba
-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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
b
⇒
a
2
ba
[1]
# ab:aaaab=aaba ab aaaab=aaba