#3457 ⟨
a
,
b
,
c
|
ba
=
ac
,
acc
=
c
⟩
Up:
Monoid enumeration
Prev:
#3456
⟨
a
,
b
,
c
|
ba
=
ac
,
acc
=
b
⟩
Next:
#3464
⟨
a
,
b
,
c
|
ba
=
ac
,
bbb
=
b
⟩
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:
ac
⋅
c
=
c
and 1 ⋅
c
=
c
, however
ac
≠ 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
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ac
[1]
2.
bc
⇒
c
2
[3]
3.
a
c
2
⇒
c
[2]
# abc:ba=ac,acc=c acb - - ba=ac bc=cc acc=c