#14728 ⟨
a
,
b
|
aabb
=
a
,
bbbbb
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#14725
⟨
a
,
b
|
aabb
=
a
,
bbbba
=
a
⟩
Next:
#14729
⟨
a
,
b
|
abab
=
a
,
aaaaa
=
a
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
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.
a
3
⇒
a
[6]
2.
a
b
2
⇒
a
2
[5]
3.
b
5
⇒
b
[2]
# ab:aabb=a,bbbbb=b ab aaa=a abb=aa bbbbb=b