#3054 ⟨
a
,
b
,
c
|
aba
=
c
,
bac
=
c
⟩
Up:
Monoid enumeration
Prev:
#3051
⟨
a
,
b
,
c
|
aba
=
c
,
bab
=
c
⟩
Next:
#3056
⟨
a
,
b
,
c
|
aba
=
c
,
cbc
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
bc
⋅
c
=
c
and 1 ⋅
c
=
c
, however
bc
≠ 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
c
<
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
c
2
[4]
2.
abc
⇒
cba
[3]
3.
aba
⇒
c
[1]
4.
b
c
2
⇒
c
[5]
# abc:aba=c,bac=c cab - - ac=cc abc=cba aba=c bcc=c