#4029 ⟨
a
,
b
|
aba
=
aab
,
abbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#4025
⟨
a
,
b
|
aba
=
aab
,
aabb
=1⟩
Next:
#4037
⟨
a
,
b
|
aba
=
aab
,
bbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-commutative monoid
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.
aba
⇒
a
2
b
[1]
2.
a
b
3
⇒ 1
[2]
3.
a
2
b
2
a
⇒
a
3
b
2
[3]
# ab:aba=aab,abbb=1 ab aba=aab abbb=1 aabba=aaabb