#6107 ⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
aa
⟩
Up:
Monoid enumeration
Prev:
#6106
⟨
a
,
b
,
c
|
ab
=
c
,
cac
=
cc
⟩
Next:
#6109
⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
ac
⟩
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
⋅
b
(
ab
)
2
=
a
2
and
a
⋅
a
=
a
2
, however
b
(
ab
)
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(
b
) = deg(
a
) = 0,
b
<
a
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
b
⇒
ab
a
2
[3]
2.
(
ab
)
3
⇒
a
2
[2]
3.
c
⇒
ab
[1]
# abc:ab=c,ccc=aa ba/c - - aaab=abaa ababab=aa c=ab