#5204 ⟨
a
,
b
,
c
|
aa
=
b
,
acbb
=
c
⟩
Up:
Monoid enumeration
Prev:
#5203
⟨
a
,
b
,
c
|
aa
=
b
,
acbb
=
b
⟩
Next:
#5206
⟨
a
,
b
,
c
|
aa
=
b
,
acbc
=
b
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaabab
-1
⟩
Embedding:
φ
(
a
) =
a
,
φ
(
b
) =
aa
,
φ
(
c
) =
b
-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(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
a
4
⇒
c
[2]
2.
c
2
a
4
⇒
ac
a
3
c
[3]
3.
b
⇒
a
2
[1]
# abc:aa=b,acbb=c ac/b - - acaaaa=c ccaaaa=acaaac b=aa