#3222 ⟨
a
,
b
|
abaabbbabab
=1⟩
Up:
Monoid enumeration
Prev:
#3205
⟨
a
,
b
|
abaabaabbab
=1⟩
Next:
#3305
⟨
a
,
b
|
aaaaaaaaaa
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
a
2
b
2
(
ba
)
3
=
a
and
a
⋅ 1 =
a
, however
b
a
2
b
2
(
ba
)
3
≠ 1
Not right cancellative, because right multiplication by
b
is not injective:
ab
a
2
b
2
⋅
b
=
a
2
b
3
ab
and
a
2
b
3
a
⋅
b
=
a
2
b
3
ab
, however
ab
a
2
b
2
≠
a
2
b
3
a
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
a
2
b
3
⇒
a
2
b
3
ab
[5]
2.
a
2
b
3
(
ab
)
3
⇒ 1
[3]
# ab:abaabbbabab=1 ab - - abaabbb=aabbbab aabbbababab=1