#2009 ⟨
a
,
b
,
c
|
abc
=
ca
,
bab
=1⟩
Up:
Monoid enumeration
Prev:
#2008
⟨
a
,
b
,
c
|
abc
=
ca
,
baa
=1⟩
Next:
#2010
⟨
a
,
b
,
c
|
abc
=
ca
,
bba
=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(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
⇒
ab
[3]
2.
a
b
2
⇒ 1
[4]
3.
ac
⇒
c
a
2
[6]
4.
bc
⇒
c
b
2
[7]
# abc:abc=ca,bab=1 ab/c - - ba=ab abb=1 ac=caa bc=cbb