#5924 ⟨
a
,
b
|
abbaab
=
bbaaa
⟩
Up:
Monoids with two generators and one relation
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#5923
⟨
a
,
b
|
abbaab
=
babaa
⟩
Next:
#5925
⟨
a
,
b
|
abbbba
=
aaaaa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite cancellative non-commutative monoid
Submonoid of enveloping group: ⟨
a
,
b
|
aaabba
-1
b
-1
b
-1
a
-1
a
-1
b
-1
⟩
Embedding:
φ
(
a
) =
a
-1
,
φ
(
b
) =
b
-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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
a
3
⇒
a
b
2
a
2
b
[1]
# ab:abbaab=bbaaa b/a bbaaa=abbaab