#1883 ⟨
a
,
b
,
c
|
aba
=
bc
,
ccc
=1⟩
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Monoid enumeration
Prev:
#1882
⟨
a
,
b
,
c
|
aba
=
bc
,
ccb
=1⟩
Next:
#1884
⟨
a
,
b
,
c
|
aba
=
ca
,
baa
=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.
bc
⇒
aba
[1]
2.
aba
c
2
⇒
b
[3]
3.
c
3
⇒ 1
[2]
# abc:aba=bc,ccc=1 ab/c - - bc=aba abacc=b ccc=1