#1438 ⟨
a
,
b
,
c
|
ab
=1,
aaa
=
cb
⟩
Up:
Monoid enumeration
Prev:
#1435
⟨
a
,
b
,
c
|
ab
=1,
aaa
=
ac
⟩
Next:
#1439
⟨
a
,
b
,
c
|
ab
=1,
aaa
=
cc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
b
4
c
=
c
and
c
⋅ 1 =
c
, however
b
4
c
≠ 1
Not right cancellative, because right multiplication by
b
4
is not injective:
b
4
c
⋅
b
4
=
b
4
and 1 ⋅
b
4
=
b
4
, however
b
4
c
≠ 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:
Left-to-right recursive path with deg(
c
) = deg(
b
) = 0,
c
<
b
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
c
b
2
cb
⇒
cbc
b
2
[8]
2.
c
b
4
⇒ 1
[6]
3.
c
b
3
cb
⇒
cbc
b
3
[7]
4.
a
⇒
c
b
3
[5]
# abc:ab=1,aaa=cb cb/a - - cbbcb=cbcbb cbbbb=1 cbbbcb=cbcbbb a=cbbb