#3024 ⟨
a
,
b
,
c
|
aba
=
a
,
cbc
=
a
⟩
Up:
Monoid enumeration
Prev:
#3021
⟨
a
,
b
,
c
|
aba
=
a
,
bcb
=
c
⟩
Next:
#3025
⟨
a
,
b
,
c
|
aba
=
a
,
cbc
=
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
c
is not injective:
c
⋅ (
bc
)
3
=
cbc
and
c
⋅
bc
=
cbc
, however (
bc
)
3
≠
bc
Not right cancellative, because right multiplication by
c
is not injective:
(
cb
)
3
⋅
c
=
cbc
and
cb
⋅
c
=
cbc
, however (
cb
)
3
≠
cb
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.
c
(
bc
)
3
⇒
cbc
[4]
2.
a
⇒
cbc
[2]
# abc:aba=a,cbc=a bc/a - - cbcbcbc=cbc a=cbc