#413 ⟨
a
,
b
,
c
|
abc
=
b
,
bbc
=1⟩
Up:
Monoid enumeration
Prev:
#412
⟨
a
,
b
,
c
|
abc
=
b
,
bbb
=1⟩
Next:
#416
⟨
a
,
b
,
c
|
abc
=
b
,
caa
=1⟩
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
b
is not injective:
b
⋅
bcb
=
b
and
b
⋅ 1 =
b
, however
bcb
≠ 1
Not right cancellative, because right multiplication by
bc
is not injective:
bcb
⋅
bc
=
bc
and 1 ⋅
bc
=
bc
, however
bcb
≠ 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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
abc
⇒
b
[1]
2.
b
2
c
⇒ 1
[2]
# abc:abc=b,bbc=1 abc - - abc=b bbc=1