#6046 ⟨
a
,
b
,
c
|
ab
=
c
,
acb
=
cc
⟩
Up:
Monoid enumeration
Prev:
#6045
⟨
a
,
b
,
c
|
ab
=
c
,
acb
=
bc
⟩
Next:
#6051
⟨
a
,
b
,
c
|
ab
=
c
,
acc
=
bb
⟩
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
a
is not injective:
a
⋅
a
b
2
= (
ab
)
2
and
a
⋅
bab
= (
ab
)
2
, however
a
b
2
≠
bab
Not right cancellative, because right multiplication by
b
is not injective:
a
2
b
⋅
b
= (
ab
)
2
and
aba
⋅
b
= (
ab
)
2
, however
a
2
b
≠
aba
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(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
2
⇒ (
ab
)
2
[2]
2.
c
⇒
ab
[1]
# abc:ab=c,acb=cc ba/c - - aabb=abab c=ab