#1929 ⟨
a
,
b
,
c
|
abc
=
aa
,
ccc
=1⟩
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Monoid enumeration
Prev:
#1928
⟨
a
,
b
,
c
|
abc
=
aa
,
ccb
=1⟩
Next:
#1930
⟨
a
,
b
,
c
|
abc
=
ab
,
aca
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
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
c
2
and
a
⋅
a
c
2
=
a
2
c
2
, however
b
≠
a
c
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
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
c
3
⇒ 1
[2]
2.
ab
⇒
a
2
c
2
[3]
# abc:abc=aa,ccc=1 ac/b - - ccc=1 ab=aacc