#13270 ⟨
a
,
b
|
bba
=
abb
,
bbb
=
aa
⟩
Up:
Monoid enumeration
Prev:
#13269
⟨
a
,
b
|
bab
=
baa
,
bba
=
bb
⟩
Next:
#13271
⟨
a
,
b
|
bba
=
abb
,
bbb
=
ab
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
bab
⋅
b
=
a
b
3
and
a
b
2
⋅
b
=
a
b
3
, however
bab
≠
a
b
2
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ba
b
2
⇒
a
b
3
[3]
2.
b
2
a
⇒
a
b
2
[1]
3.
a
2
⇒
b
3
[2]
# ab:bba=abb,bbb=aa b/a - - babb=abbb bba=abb aa=bbb