#4480 ⟨
a
,
b
,
c
|
aba
=1,
cccc
=
c
⟩
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Monoid enumeration
Prev:
#4477
⟨
a
,
b
,
c
|
aba
=1,
cbcc
=
c
⟩
Next:
#4484
⟨
a
,
b
,
c
|
abc
=1,
aaab
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Isomorphic to ℕ
(4 = 1)
∗ ℤ
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
c
3
=
c
and
c
⋅ 1 =
c
, however
c
3
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
c
3
⋅
c
=
c
and 1 ⋅
c
=
c
, however
c
3
≠ 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.
ba
⇒
ab
[3]
2.
a
2
b
⇒ 1
[4]
3.
c
4
⇒
c
[2]
# abc:aba=1,cccc=c abc - - ba=ab aab=1 cccc=c