#1928 ⟨
a
,
b
,
c
|
abc
=
aa
,
ccb
=1⟩
Up:
Monoid enumeration
Prev:
#1925
⟨
a
,
b
,
c
|
abc
=
aa
,
cbb
=1⟩
Next:
#1929
⟨
a
,
b
,
c
|
abc
=
aa
,
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
c
is not injective:
c
⋅
cbc
=
c
and
c
⋅ 1 =
c
, however
cbc
≠ 1
Not right cancellative, because right multiplication by
cb
is not injective:
cbc
⋅
cb
=
cb
and 1 ⋅
cb
=
cb
, 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.
abc
⇒
a
2
[1]
2.
c
2
b
⇒ 1
[2]
3.
a
2
cb
⇒
ab
[3]
# abc:abc=aa,ccb=1 abc - - abc=aa ccb=1 aacb=ab