#2810 ⟨
a
,
b
,
c
|
aaa
=
a
,
bbc
=
a
⟩
Up:
Monoid enumeration
Prev:
#2808
⟨
a
,
b
,
c
|
aaa
=
a
,
bac
=
b
⟩
Next:
#2811
⟨
a
,
b
,
c
|
aaa
=
a
,
bbc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
bc
(
b
2
c
)
2
=
b
2
c
and
b
⋅
bc
=
b
2
c
, however
bc
(
b
2
c
)
2
≠
bc
Not right cancellative, because right multiplication by
c
is not injective:
b
2
(
c
b
2
)
2
⋅
c
=
b
2
c
and
b
2
⋅
c
=
b
2
c
, however
b
2
(
c
b
2
)
2
≠
b
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(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
b
2
c
)
3
⇒
b
2
c
[4]
2.
a
⇒
b
2
c
[2]
# abc:aaa=a,bbc=a bc/a - - bbcbbcbbc=bbc a=bbc