#1899 ⟨
a
,
b
,
c
|
aba
=
cc
,
bcc
=1⟩
Up:
Monoid enumeration
Prev:
#1897
⟨
a
,
b
,
c
|
aba
=
cc
,
bbc
=1⟩
Next:
#1910
⟨
a
,
b
,
c
|
abc
=
aa
,
acb
=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
⋅
c
2
b
=
b
and
b
⋅ 1 =
b
, however
c
2
b
≠ 1
Not right cancellative, because right multiplication by
a
is not injective:
cbc
⋅
a
=
a
and 1 ⋅
a
=
a
, however
cbc
≠ 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
⇒
c
2
[1]
2.
b
c
2
⇒ 1
[2]
3.
cba
⇒
bca
[4]
4.
cbca
⇒
a
[5]
# abc:aba=cc,bcc=1 abc - - aba=cc bcc=1 cba=bca cbca=a