#5516 ⟨
a
,
b
|
aaaabb
=
abbbb
⟩
Up:
Monoids with two generators and one relation
Prev:
#5515
⟨
a
,
b
|
aaaabb
=
abbba
⟩
Next:
#5517
⟨
a
,
b
|
aaaabb
=
baaaa
⟩
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
⋅
a
3
b
2
=
a
b
4
and
a
⋅
b
4
=
a
b
4
, however
a
3
b
2
≠
b
4
Not right cancellative, because right multiplication by
b
is not injective:
a
4
b
⋅
b
=
a
b
4
and
a
b
3
⋅
b
=
a
b
4
, however
a
4
b
≠
a
b
3
Reduced enveloping group: ⟨
a
,
b
|
aaabb
=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
2
⇒
a
b
4
[1]
# ab:aaaabb=abbbb ab aaaabb=abbbb