#1052 ⟨
a
,
b
|
aaabba
=
abb
⟩
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Monoid enumeration
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#1051
⟨
a
,
b
|
aaabba
=
aba
⟩
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#1053
⟨
a
,
b
|
aaabba
=
baa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
c
is not injective:
c
⋅
b
2
= (
ca
)
2
and
c
⋅
aca
= (
ca
)
2
, however
b
2
≠
aca
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
Auxiliary generators:
c
=
abb
Reduction order:
Left-to-right 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.
a
2
c
2
⇒ (
ca
)
2
[6]
2.
a
2
ca
⇒
c
[4]
3.
c
b
2
⇒ (
ca
)
2
[7]
4.
a
b
2
⇒
c
[2]
# ab:aaabba=abb ca/b abb=c magic:0 aacc=caca aaca=c cbb=caca abb=c