#560 ⟨
a
,
b
,
c
|
bb
=
ac
,
cc
=
c
⟩
Up:
Monoid enumeration
Prev:
#559
⟨
a
,
b
,
c
|
bb
=
ac
,
cc
=
b
⟩
Next:
#561
⟨
a
,
b
,
c
|
bc
=
ac
,
cc
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
c
=
c
and
c
⋅ 1 =
c
, however
c
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
c
⋅
c
=
c
and 1 ⋅
c
=
c
, however
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 shortlex with
b
<
a
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
b
2
[1]
2.
c
2
⇒
c
[2]
3.
b
2
c
⇒
b
2
[3]
# abc:bb=ac,cc=c bac - - ac=bb cc=c bbc=bb