#4168 ⟨
a
,
b
|
abb
=
aba
,
bba
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#4165
⟨
a
,
b
|
abb
=
aba
,
baa
=
b
⟩
Next:
#4171
⟨
a
,
b
|
abb
=
aba
,
bbb
=
b
⟩
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
⇒
a
[2]
2.
aba
⇒
a
b
2
[1]
3.
a
b
4
⇒
a
b
2
[3]
# ab:abb=aba,bba=a ba bba=a aba=abb abbbb=abb