#5047 ⟨
a
,
b
|
aaababa
=
baba
⟩
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Monoid enumeration
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#5046
⟨
a
,
b
|
aaababa
=
baab
⟩
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#5048
⟨
a
,
b
|
aaababa
=
babb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
3
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
3
≠ 1
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
=
baba
Reduction order:
Left-to-right shortlex with
a
<
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
bac
⇒
cba
[5]
2.
a
3
c
⇒
c
[4]
3.
(
ba
)
2
⇒
c
[2]
4.
babc
⇒
c
a
2
c
[6]
# ab:aaababa=baba acb baba=c magic:0 bac=cba aaac=c baba=c babc=caac