#1669 ⟨
a
,
b
,
c
|
aab
=
ba
,
cac
=1⟩
Up:
Monoid enumeration
Prev:
#1668
⟨
a
,
b
,
c
|
aab
=
ba
,
cab
=1⟩
Next:
#1670
⟨
a
,
b
,
c
|
aab
=
ba
,
cba
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-commutative monoid
Element
a
has infinite order
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(
c
) = deg(
a
) = 0,
c
<
a
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ca
[3]
2.
c
2
a
⇒ 1
[4]
3.
c
2
b
⇒
ab
c
2
[7]
4.
a
2
b
⇒
ba
[1]
# abc:aab=ba,cac=1 ca/b - - ac=ca cca=1 ccb=abcc aab=ba