#2029 ⟨
a
,
b
|
abaaabab
=
bb
⟩
Up:
Monoids with two generators and one relation
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#2028
⟨
a
,
b
|
abaaabab
=
ba
⟩
Next:
#2030
⟨
a
,
b
|
abaaabba
=
aa
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
3
ba
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
ab
a
3
ba
≠
b
Enveloping group: ⟨
a
,
b
|
aaabb
⟩
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.
ab
a
3
b
3
⇒
b
2
a
3
bab
[2]
2.
ab
a
3
bab
⇒
b
2
[1]
# ab:abaaabab=bb ba abaaabbb=bbaaabab abaaabab=bb