#1415 ⟨
a
,
b
,
c
|
aa
=1,
bac
=
bc
⟩
Up:
Monoid enumeration
Prev:
#1414
⟨
a
,
b
,
c
|
aa
=1,
bac
=
bb
⟩
Next:
#1416
⟨
a
,
b
,
c
|
aa
=1,
bac
=
cb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
ac
=
bc
and
b
⋅
c
=
bc
, however
ac
≠
c
Not right cancellative, because right multiplication by
c
is not injective:
ba
⋅
c
=
bc
and
b
⋅
c
=
bc
, however
ba
≠
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.
a
2
⇒ 1
[1]
2.
bac
⇒
bc
[2]
# abc:aa=1,bac=bc abc - - aa=1 bac=bc