#1863 ⟨
a
,
b
,
c
|
aba
=
bc
,
aca
=1⟩
Up:
Monoid enumeration
Prev:
#1860
⟨
a
,
b
,
c
|
aba
=
bb
,
ccc
=1⟩
Next:
#1864
⟨
a
,
b
,
c
|
aba
=
bc
,
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:
Right-to-left recursive path with deg(
a
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
ca
[3]
2.
c
a
2
⇒ 1
[4]
3.
bc
⇒
aba
[1]
4.
b
a
3
⇒
cab
[6]
# abc:aba=bc,aca=1 reversed:ac/b - - ac=ca caa=1 bc=aba baaa=cab