#5154 ⟨
a
,
b
,
c
|
aa
=
a
,
bcbc
=
a
⟩
Up:
Monoid enumeration
Prev:
#5153
⟨
a
,
b
,
c
|
aa
=
a
,
bbcc
=
b
⟩
Next:
#5155
⟨
a
,
b
,
c
|
aa
=
a
,
bcbc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
b
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
c
(
bc
)
3
= (
bc
)
2
and
b
⋅
cbc
= (
bc
)
2
, however
c
(
bc
)
3
≠
cbc
Not right cancellative, because right multiplication by
c
is not injective:
b
(
cb
)
3
⋅
c
= (
bc
)
2
and
bcb
⋅
c
= (
bc
)
2
, however
b
(
cb
)
3
≠
bcb
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 recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
bc
)
4
⇒ (
bc
)
2
[4]
2.
a
⇒ (
bc
)
2
[2]
# abc:aa=a,bcbc=a bc/a - - bcbcbcbc=bcbc a=bcbc