#16325 ⟨
a
,
b
|
aab
=
bb
,
bbab
=
aa
⟩
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Monoid enumeration
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#16324
⟨
a
,
b
|
aab
=
bb
,
bbaa
=
bb
⟩
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#16328
⟨
a
,
b
|
aab
=
bb
,
bbab
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅ (
ab
)
2
=
a
2
and
a
⋅
a
=
a
2
, however (
ab
)
2
≠
a
Not right cancellative, because right multiplication by
b
is not injective:
b
⋅
b
=
a
2
b
and
a
2
⋅
b
=
a
2
b
, however
b
≠
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 recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
7
⇒
a
2
[7]
2.
b
a
2
⇒
a
4
[5]
3.
b
2
⇒
a
2
b
[1]
4.
a
(
ab
)
2
⇒
a
2
[2]
# ab:aab=bb,bbab=aa a/b - - aaaaaaa=aa baa=aaaa bb=aab aabab=aa