#1806 ⟨
a
,
b
|
abbaabbba
=
b
⟩
Up:
Monoids with two generators and one relation
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#1805
⟨
a
,
b
|
abbaabbba
=
a
⟩
Next:
#1807
⟨
a
,
b
|
abbabaaab
=
a
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aaabbaaba
-1
b
⟩
Embedding:
φ
(
a
) =
aba
,
φ
(
b
) =
a
-1
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
b
2
a
2
b
4
⇒
b
3
a
2
b
3
a
[2]
2.
a
b
2
a
2
b
3
a
⇒
b
[1]
# ab:abbaabbba=b ba abbaabbbb=bbbaabbba abbaabbba=b