#5122 ⟨
a
,
b
|
aabaaab
=
abab
⟩
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Monoids with two generators and one relation
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#5121
⟨
a
,
b
|
aabaaab
=
abaa
⟩
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#5123
⟨
a
,
b
|
aabaaab
=
abba
⟩
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
a
3
b
⇒ (
ab
)
2
[1]
2.
(
a
2
b
)
2
ab
⇒ (
ab
)
2
a
3
b
[2]
# ab:aabaaab=abab ba aabaaab=abab aabaabab=ababaaab