#1552 ⟨
a
,
b
|
aaaaaaaba
=
b
⟩
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Monoids with two generators and one relation
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#1551
⟨
a
,
b
|
aaaaaaaba
=
a
⟩
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#1553
⟨
a
,
b
|
aaaaaaabb
=
a
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aaaaaaabab
-1
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
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
7
b
2
⇒
b
a
6
ba
[2]
2.
a
7
ba
⇒
b
[1]
# ab:aaaaaaaba=b ba aaaaaaabb=baaaaaaba aaaaaaaba=b