#1877 ⟨
a
,
b
,
c
|
aba
=
bc
,
cac
=1⟩
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Monoid enumeration
Prev:
#1876
⟨
a
,
b
,
c
|
aba
=
bc
,
cab
=1⟩
Next:
#1879
⟨
a
,
b
,
c
|
aba
=
bc
,
cbb
=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:
Right-to-left 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.
ca
⇒
ac
[3]
2.
a
c
2
⇒ 1
[4]
3.
ba
⇒
c
2
bc
[7]
4.
b
c
3
⇒
ab
[5]
# abc:aba=bc,cac=1 reversed:ca/b - - ca=ac acc=1 ba=ccbc bccc=ab