#20038 ⟨
a
,
b
|
aab
=
a
,
bbba
=
bba
⟩
Up:
Monoids with two generators and two relations
Prev:
#19917
⟨
a
,
b
|
aaa
=
b
,
bbbb
=
abb
⟩
Next:
#20046
⟨
a
,
b
|
aab
=
a
,
bbbb
=
bba
⟩
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
2
⇒
a
[6]
2.
ab
⇒
a
[7]
3.
b
3
a
⇒
b
2
a
[2]
# ab:aab=a,bbba=bba ab aa=a ab=a bbba=bba