#6252 ⟨
a
,
b
,
c
|
aa
=1,
bbbccc
=1⟩
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Monoid enumeration
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#6251
⟨
a
,
b
,
c
|
aa
=1,
bbbccb
=1⟩
Next:
#6253
⟨
a
,
b
,
c
|
aa
=1,
bbcabc
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
b
2
c
3
b
=
b
and
b
⋅ 1 =
b
, however
b
2
c
3
b
≠ 1
Not right cancellative, because right multiplication by
b
2
c
3
is not injective:
b
2
c
3
b
⋅
b
2
c
3
=
b
2
c
3
and 1 ⋅
b
2
c
3
=
b
2
c
3
, however
b
2
c
3
b
≠ 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 shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
b
3
c
3
⇒ 1
[2]
# abc:aa=1,bbbccc=1 abc - - aa=1 bbbccc=1