#4384 ⟨
a
,
b
,
c
|
aba
=1,
aacc
=
c
⟩
Up:
Monoid enumeration
Prev:
#4378
⟨
a
,
b
,
c
|
aba
=1,
aaca
=
c
⟩
Next:
#4402
⟨
a
,
b
,
c
|
aba
=1,
abcc
=
c
⟩
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:
b
⋅
c
=
c
2
and
c
⋅
c
=
c
2
, however
b
≠
c
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
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[3]
2.
bc
⇒
c
2
[4]
3.
a
2
b
⇒ 1
[5]
4.
a
2
c
2
⇒
c
[2]
# abc:aba=1,aacc=c acb - - ba=ab bc=cc aab=1 aacc=c