#521 ⟨
a
,
b
,
c
|
ac
=
ab
,
ba
=
b
⟩
Up:
Monoid enumeration
Prev:
#520
⟨
a
,
b
,
c
|
ac
=
ab
,
ba
=
a
⟩
Next:
#522
⟨
a
,
b
,
c
|
ac
=
ab
,
ba
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
=
b
and
b
⋅ 1 =
b
, however
a
≠ 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.
ac
⇒
ab
[1]
2.
ba
⇒
b
[2]
3.
bc
⇒
b
2
[3]
# abc:ac=ab,ba=b abc - - ac=ab ba=b bc=bb