#3577 ⟨
a
,
b
,
c
|
ac
=
ab
,
ca
=
ba
⟩
Up:
Monoid enumeration
Prev:
#3576
⟨
a
,
b
,
c
|
ac
=
ab
,
bc
=
ba
⟩
Next:
#3578
⟨
a
,
b
,
c
|
ac
=
ab
,
ca
=
bb
⟩
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
a
is not injective:
a
⋅
c
=
ab
and
a
⋅
b
=
ab
, however
c
≠
b
Not right cancellative, because right multiplication by
a
is not injective:
c
⋅
a
=
ba
and
b
⋅
a
=
ba
, however
c
≠
b
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.
ca
⇒
ba
[2]
# abc:ac=ab,ca=ba abc - - ac=ab ca=ba