#5878 ⟨
a
,
b
|
aabb
=1,
abaab
=
a
⟩
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Monoids with two generators and two relations
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#5873
⟨
a
,
b
|
aabb
=1,
aabab
=
b
⟩
Next:
#5900
⟨
a
,
b
|
abab
=1,
aaabb
=
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
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
⇒ 1
[1]
2.
a
3
b
⇒
ab
a
2
[3]
3.
ab
a
2
b
⇒
a
[2]
# ab:aabb=1,abaab=a ba aabb=1 aaab=abaa abaab=a