#5612 ⟨
a
,
b
|
aaabba
=
abbbb
⟩
Up:
Monoids with two generators and one relation
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#5611
⟨
a
,
b
|
aaabba
=
abbba
⟩
Next:
#5613
⟨
a
,
b
|
aaabba
=
baaaa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
a
2
b
2
a
=
a
b
4
and
a
⋅
b
4
=
a
b
4
, however
a
2
b
2
a
≠
b
4
Enveloping group: ⟨
a
,
b
|
aaaabba
-1
a
-1
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
4
⇒
a
3
b
2
a
[1]
# ab:aaabba=abbbb a/b abbbb=aaabba