#1871 ⟨
a
,
b
,
c
|
aba
=
bc
,
bbc
=1⟩
Up:
Monoid enumeration
Prev:
#1869
⟨
a
,
b
,
c
|
aba
=
bc
,
bba
=1⟩
Next:
#1874
⟨
a
,
b
,
c
|
aba
=
bc
,
bcc
=1⟩
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
b
is not injective:
b
⋅ (
ab
)
2
=
b
and
b
⋅ 1 =
b
, however (
ab
)
2
≠ 1
Not right cancellative, because right multiplication by
aba
is not injective:
(
ab
)
2
⋅
aba
=
aba
and 1 ⋅
aba
=
aba
, however (
ab
)
2
≠ 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 recursive path with deg(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
(
ba
)
2
⇒ 1
[2]
2.
bc
⇒
aba
[1]
# abc:aba=bc,bbc=1 ab/c - - baba=1 bc=aba