#2596 ⟨
a
,
b
,
c
|
aba
=
b
,
aaca
=1⟩
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Monoid enumeration
Prev:
#2595
⟨
a
,
b
,
c
|
aba
=
b
,
aabc
=1⟩
Next:
#2598
⟨
a
,
b
,
c
|
aba
=
b
,
aacc
=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(
c
) = 0,
a
<
c
; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ca
⇒
ac
[6]
2.
a
3
c
⇒ 1
[9]
3.
ab
⇒
b
a
2
c
[4]
4.
cb
⇒
b
a
3
[8]
# abc:aba=b,aaca=1 ac/b - - ca=ac aaac=1 ab=baac cb=baaa