#5853 ⟨
a
,
b
|
abaaba
=
abbba
⟩
Up:
Monoid enumeration
Prev:
#5852
⟨
a
,
b
|
abaaba
=
abbab
⟩
Next:
#5854
⟨
a
,
b
|
abaaba
=
abbbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
b
a
2
ba
=
a
b
3
a
and
a
⋅
b
3
a
=
a
b
3
a
, however
b
a
2
ba
≠
b
3
a
Not right cancellative, because right multiplication by
a
is not injective:
ab
a
2
b
⋅
a
=
a
b
3
a
and
a
b
3
⋅
a
=
a
b
3
a
, however
ab
a
2
b
≠
a
b
3
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
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
b
3
a
⇒ (
aba
)
2
[1]
# ab:abaaba=abbba a/b - - abbba=abaaba