#1110 ⟨
a
,
b
|
abaaab
=
bbb
⟩
Up:
Monoid enumeration
Prev:
#1109
⟨
a
,
b
|
abaaab
=
bba
⟩
Next:
#1111
⟨
a
,
b
|
abaaba
=
aaa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
3
⋅
b
=
b
3
and
b
2
⋅
b
=
b
3
, however
ab
a
3
≠
b
2
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.
ab
a
3
b
⇒
b
3
[1]
2.
ab
a
2
b
3
⇒
b
3
a
3
b
[2]
# ab:abaaab=bbb ba - - abaaab=bbb abaabbb=bbbaaab