#2215 ⟨
a
,
b
|
aabaaba
=
aaa
⟩
Up:
Monoid enumeration
Prev:
#2214
⟨
a
,
b
|
aabaaab
=
bbb
⟩
Next:
#2216
⟨
a
,
b
|
aabaaba
=
aab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
aba
)
2
=
a
3
and
a
⋅
a
2
=
a
3
, however (
aba
)
2
≠
a
2
Not right cancellative, because right multiplication by
a
is not injective:
(
a
2
b
)
2
⋅
a
=
a
3
and
a
2
⋅
a
=
a
3
, however (
a
2
b
)
2
≠
a
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.
a
4
ba
⇒
a
2
b
a
3
[2]
2.
(
a
2
b
)
2
a
⇒
a
3
[1]
# ab:aabaaba=aaa ba - - aaaaba=aabaaa aabaaba=aaa