#4423 ⟨
a
,
b
,
c
|
aba
=1,
accc
=
c
⟩
Up:
Monoid enumeration
Prev:
#4420
⟨
a
,
b
,
c
|
aba
=1,
accb
=
c
⟩
Next:
#4444
⟨
a
,
b
,
c
|
aba
=1,
bbbc
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
c
2
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
c
2
≠ 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
) = 0; deg(
a
) = deg(
b
) = 1,
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
c
3
⇒
c
[2]
2.
bc
⇒
c
5
[5]
3.
ba
⇒
ab
[3]
4.
a
2
b
⇒ 1
[6]
# abc:aba=1,accc=c c/ab - - accc=c bc=ccccc ba=ab aab=1