#552 ⟨
a
,
b
|
abbba
=
aab
⟩
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Monoid enumeration
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#551
⟨
a
,
b
|
abbba
=
aaa
⟩
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#553
⟨
a
,
b
|
abbba
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
3
a
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
b
3
a
≠
ab
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
a
b
3
a
[1]
# ab:abbba=aab reversed:b/a - - aab=abbba