#12988 ⟨
a
,
b
|
abb
=
aaa
,
bbaa
=
a
⟩
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Monoid enumeration
Prev:
#12985
⟨
a
,
b
|
abb
=
aaa
,
baba
=
b
⟩
Next:
#12992
⟨
a
,
b
|
abb
=
aaa
,
bbba
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
6
=
a
and
a
⋅ 1 =
a
, however
b
6
≠ 1
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
6
⇒
a
[11]
2.
b
2
a
⇒
a
b
2
[13]
3.
a
2
⇒
a
b
4
[12]
# ab:abb=aaa,bbaa=a b/a - - abbbbbb=a bba=abb aa=abbbb