#1983 ⟨
a
,
b
,
c
|
abc
=
ba
,
cca
=1⟩
Up:
Monoid enumeration
Prev:
#1979
⟨
a
,
b
,
c
|
abc
=
ba
,
cac
=1⟩
Next:
#1984
⟨
a
,
b
,
c
|
abc
=
ba
,
ccb
=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
c
is not injective:
c
⋅
cac
=
c
and
c
⋅ 1 =
c
, however
cac
≠ 1
Not right cancellative, because right multiplication by
ca
is not injective:
cac
⋅
ca
=
ca
and 1 ⋅
ca
=
ca
, however
cac
≠ 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
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
abc
[1]
2.
c
2
a
⇒ 1
[2]
# abc:abc=ba,cca=1 bc/a - - ba=abc cca=1