#5170 ⟨
a
,
b
|
aababaa
=
abba
⟩
Up:
Monoid enumeration
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#5169
⟨
a
,
b
|
aababaa
=
abab
⟩
Next:
#5171
⟨
a
,
b
|
aababaa
=
abbb
⟩
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
⋅ (
ab
)
2
a
2
=
a
b
2
a
and
a
⋅
b
2
a
=
a
b
2
a
, however (
ab
)
2
a
2
≠
b
2
a
Not right cancellative, because right multiplication by
a
is not injective:
a
2
(
ba
)
2
⋅
a
=
a
b
2
a
and
a
b
2
⋅
a
=
a
b
2
a
, however
a
2
(
ba
)
2
≠
a
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
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
(
ab
)
2
a
2
⇒
a
b
2
a
[1]
2.
ab
(
ba
)
3
a
⇒
a
(
ab
)
3
ba
[2]
# ab:aababaa=abba ab - - aababaa=abba abbababaa=aabababba