#559 ⟨
a
,
b
|
aaba
=
aaab
⟩
Up:
Monoid enumeration
Prev:
#558
⟨
a
,
b
|
aaba
=
aaaa
⟩
Next:
#560
⟨
a
,
b
|
aabb
=
aaaa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
aba
=
a
3
b
and
a
⋅
a
2
b
=
a
3
b
, however
aba
≠
a
2
b
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
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
3
b
⇒
a
2
ba
[1]
# ab:aaba=aaab ba - - aaab=aaba