#2023 ⟨
a
,
b
,
c
|
abc
=
cb
,
ccc
=1⟩
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Monoid enumeration
Prev:
#2021
⟨
a
,
b
,
c
|
abc
=
cb
,
bcc
=1⟩
Next:
#2024
⟨
a
,
b
,
c
|
abc
=
cc
,
acc
=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.
c
3
⇒ 1
[2]
2.
ab
⇒
cb
c
2
[3]
# abc:abc=cb,ccc=1 ca/b - - ccc=1 ab=cbcc