#3428 ⟨
a
,
b
,
c
|
ba
=
ab
,
acc
=
b
⟩
Up:
Monoid enumeration
Prev:
#3427
⟨
a
,
b
,
c
|
ba
=
ab
,
acc
=
a
⟩
Next:
#3429
⟨
a
,
b
,
c
|
ba
=
ab
,
acc
=
c
⟩
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
c
2
=
a
c
2
a
and
a
⋅
c
2
a
=
a
c
2
a
, however
a
c
2
≠
c
2
a
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
c
2
⇒
a
c
2
a
[4]
2.
b
⇒
a
c
2
[2]
# abc:ba=ab,acc=b ca/b - - aacc=acca b=acc