#18034 ⟨
a
,
b
|
abab
=1,
aabba
=
ba
⟩
Up:
Monoids with two generators and two relations
Prev:
#18023
⟨
a
,
b
|
abab
=1,
aaabb
=
bb
⟩
Next:
#18215
⟨
a
,
b
|
aaa
=
a
,
bbbbbbb
=1⟩
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
b
2
⇒
b
[3]
2.
(
ab
)
2
⇒ 1
[1]
# ab:abab=1,aabba=ba ab aabb=b abab=1