#1664 ⟨
a
,
b
|
aabaaaaab
=
b
⟩
Up:
Monoids with two generators and one relation
Prev:
#1663
⟨
a
,
b
|
aabaaaaab
=
a
⟩
Next:
#1666
⟨
a
,
b
|
aabaaaaba
=
b
⟩
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:
a
2
b
a
5
⋅
b
=
b
and 1 ⋅
b
=
b
, however
a
2
b
a
5
≠ 1
Enveloping group is isomorphic to ℤ
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
a
3
b
⇒
a
(
ab
)
2
[3]
2.
b
a
5
b
⇒
a
4
bab
[5]
3.
a
6
bab
⇒
b
[4]
# ab:aabaaaaab=b ab baaab=aabab baaaaab=aaaabab aaaaaabab=b