#1667 ⟨
a
,
b
,
c
|
aab
=
ba
,
caa
=1⟩
Up:
Monoid enumeration
Prev:
#1666
⟨
a
,
b
,
c
|
aab
=
ba
,
bcc
=1⟩
Next:
#1668
⟨
a
,
b
,
c
|
aab
=
ba
,
cab
=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
⋅
a
2
c
=
c
and
c
⋅ 1 =
c
, however
a
2
c
≠ 1
Not right cancellative, because right multiplication by
a
2
is not injective:
a
2
c
⋅
a
2
=
a
2
and 1 ⋅
a
2
=
a
2
, however
a
2
c
≠ 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:
Right-to-left 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
a
2
⇒ 1
[2]
2.
ba
⇒
a
2
b
[1]
# abc:aab=ba,caa=1 reversed:ac/b - - caa=1 ba=aab