#12944 ⟨
a
,
b
|
aba
=
aab
,
abba
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#12932
⟨
a
,
b
|
aba
=
aab
,
aaaa
=
a
⟩
Next:
#12946
⟨
a
,
b
|
aba
=
aab
,
abbb
=
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
aba
[1]
2.
a
b
2
a
⇒
a
[2]
3.
a
(
ba
)
2
⇒
a
2
[3]
# ab:aba=aab,abba=a ba aab=aba abba=a ababa=aa