#954 ⟨
a
,
b
|
aabbaba
=
ba
⟩
Up:
Monoid enumeration
Prev:
#953
⟨
a
,
b
|
aabbaba
=
ab
⟩
Next:
#955
⟨
a
,
b
|
aabbaba
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 9
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
a
2
c
⋅
c
=
c
and 1 ⋅
c
=
c
, however
a
2
c
≠ 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
=
bba
Reduction order:
Right-to-left 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
2
c
2
⇒
c
[5]
2.
a
2
cba
⇒
ba
[3]
3.
bc
⇒
cacba
[4]
4.
b
2
a
⇒
c
[2]
# ab:aabbaba=ba reversed:ac/b bba=c morph:3/1 aacc=c aacba=ba bc=cacba bba=c