#1638 ⟨
a
,
b
|
aaabbaaab
=
b
⟩
Up:
Monoids with two generators and one relation
Prev:
#1637
⟨
a
,
b
|
aaabbaaab
=
a
⟩
Next:
#1639
⟨
a
,
b
|
aaabbaaba
=
a
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
a
3
b
2
a
3
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
3
b
2
a
3
≠ 1
Enveloping group: ⟨
a
,
b
|
aaaaaabb
⟩
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
3
b
3
⇒
b
2
a
3
b
[2]
2.
a
3
b
2
a
3
b
⇒
b
[1]
# ab:aaabbaaab=b ba aaabbb=bbaaab aaabbaaab=b