#2017 ⟨
a
,
b
,
c
|
abc
=
ca
,
cbc
=1⟩
Up:
Monoid enumeration
Prev:
#2016
⟨
a
,
b
,
c
|
abc
=
ca
,
cba
=1⟩
Next:
#2018
⟨
a
,
b
,
c
|
abc
=
ca
,
ccc
=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(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
cb
⇒
bc
[3]
2.
b
c
2
⇒ 1
[4]
3.
ba
⇒
a
c
2
[6]
4.
ca
⇒
abc
[1]
# abc:abc=ca,cbc=1 bc/a - - cb=bc bcc=1 ba=acc ca=abc