#1770 ⟨
a
,
b
,
c
|
aab
=
cc
,
aac
=1⟩
Up:
Monoid enumeration
Prev:
#1769
⟨
a
,
b
,
c
|
aab
=
cb
,
ccc
=1⟩
Next:
#1772
⟨
a
,
b
,
c
|
aab
=
cc
,
abb
=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
a
is not injective:
a
⋅
a
5
ba
=
a
and
a
⋅ 1 =
a
, however
a
5
ba
≠ 1
Not right cancellative, because right multiplication by
a
5
b
is not injective:
a
5
ba
⋅
a
5
b
=
a
5
b
and 1 ⋅
a
5
b
=
a
5
b
, however
a
5
ba
≠ 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(
b
) = deg(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
6
b
⇒ 1
[6]
2.
a
2
b
a
4
b
⇒
a
4
b
a
2
b
[5]
3.
c
⇒
a
4
b
[4]
# abc:aab=cc,aac=1 reversed:ba/c - - aaaaaab=1 aabaaaab=aaaabaab c=aaaab