#1965 ⟨
a
,
b
,
c
|
abc
=
ba
,
aca
=1⟩
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Monoid enumeration
Prev:
#1960
⟨
a
,
b
,
c
|
abc
=
ac
,
bcc
=1⟩
Next:
#1966
⟨
a
,
b
,
c
|
abc
=
ba
,
acb
=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.
b
c
3
⇒
cb
[5]
2.
ba
⇒
abc
[1]
3.
ca
⇒
ac
[3]
4.
a
2
c
⇒ 1
[6]
# abc:abc=ba,aca=1 bc/a - - bccc=cb ba=abc ca=ac aac=1