#4120 ⟨
a
,
b
|
aab
=
aaa
,
aba
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#4118
⟨
a
,
b
|
bbb
=
aaa
,
abab
=1⟩
Next:
#4122
⟨
a
,
b
|
aab
=
aaa
,
abb
=
a
⟩
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
[1]
2.
aba
⇒
a
[2]
3.
a
4
⇒
a
2
[3]
# ab:aab=aaa,aba=a ab aab=aaa aba=a aaaa=aa