#1879 ⟨
a
,
b
,
c
|
aba
=
bc
,
cbb
=1⟩
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Monoid enumeration
Prev:
#1877
⟨
a
,
b
,
c
|
aba
=
bc
,
cac
=1⟩
Next:
#1882
⟨
a
,
b
,
c
|
aba
=
bc
,
ccb
=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
c
is not injective:
c
⋅
b
2
c
=
c
and
c
⋅ 1 =
c
, however
b
2
c
≠ 1
Not right cancellative, because right multiplication by
b
2
is not injective:
b
2
c
⋅
b
2
=
b
2
and 1 ⋅
b
2
=
b
2
, however
b
2
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
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
aba
⇒
bc
[1]
2.
c
b
2
⇒ 1
[2]
3.
bcba
⇒
a
b
2
c
[3]
4.
cba
b
2
c
⇒
cba
[4]
# abc:aba=bc,cbb=1 abc - - aba=bc cbb=1 bcba=abbc cbabbc=cba