#2001 ⟨
a
,
b
,
c
|
abc
=
bc
,
bbc
=1⟩
Up:
Monoid enumeration
Prev:
#2000
⟨
a
,
b
,
c
|
abc
=
bc
,
acc
=1⟩
Next:
#2004
⟨
a
,
b
,
c
|
abc
=
bc
,
ccc
=1⟩
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
b
is not injective:
b
⋅
bcb
=
b
and
b
⋅ 1 =
b
, however
bcb
≠ 1
Not right cancellative, because right multiplication by
c
is not injective:
ab
⋅
c
=
bc
and
b
⋅
c
=
bc
, however
ab
≠
b
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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
abc
⇒
bc
[1]
2.
b
2
c
⇒ 1
[2]
# abc:abc=bc,bbc=1 abc - - abc=bc bbc=1