#3890 ⟨
a
,
b
|
aaaaabbba
=
ba
⟩
Up:
Monoid enumeration
Prev:
#3889
⟨
a
,
b
|
aaaaabbba
=
ab
⟩
Next:
#3891
⟨
a
,
b
|
aaaaabbba
=
bb
⟩
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
a
is not injective:
a
5
b
3
⋅
a
=
ba
and
b
⋅
a
=
ba
, however
a
5
b
3
≠
b
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
=
bbba
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.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
(
a
4
c
)
3
⇒
c
[4]
2.
ba
⇒
a
5
c
[3]
3.
bc
⇒
c
a
4
c
[5]
# ab:aaaaabbba=ba ac/b bbba=c morph:4/2 aaaaacaaaacaaaac=c ba=aaaaac bc=caaaac