#6752 ⟨
a
,
b
|
aba
=
a
,
baab
=
aa
⟩
Up:
Monoids with two generators and two relations
Prev:
#6751
⟨
a
,
b
|
aba
=
a
,
abbb
=
bb
⟩
Next:
#6753
⟨
a
,
b
|
aba
=
a
,
baab
=
ab
⟩
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.
a
2
b
⇒
a
3
[3]
2.
aba
⇒
a
[1]
3.
b
a
2
⇒
a
3
[4]
4.
a
4
⇒
a
2
[5]
# ab:aba=a,baab=aa ab aab=aaa aba=a baa=aaa aaaa=aa