#6109 ⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
ac
⟩
Up:
Monoid enumeration
Prev:
#6107
⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
aa
⟩
Next:
#6110
⟨
a
,
b
,
c
|
ab
=
c
,
ccc
=
ba
⟩
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
=
c
3
and
c
2
⋅
c
=
c
3
, however
a
≠
c
2
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(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ab
⇒
c
[1]
2.
ac
⇒
c
3
[2]
# abc:ab=c,ccc=ac bc/a - - ab=c ac=ccc