#20317 ⟨
a
,
b
|
aba
=
b
,
bbbb
=
abb
⟩
Up:
Monoid enumeration
Prev:
#20314
⟨
a
,
b
|
aba
=
b
,
bbbb
=
aaa
⟩
Next:
#20318
⟨
a
,
b
|
aba
=
b
,
bbbb
=
bab
⟩
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
b
is not injective:
b
⋅
ba
=
b
4
and
b
⋅
b
3
=
b
4
, however
ba
≠
b
3
Not right cancellative, because right multiplication by
b
is not injective:
ab
⋅
b
=
b
4
and
b
3
⋅
b
=
b
4
, however
ab
≠
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
7
⇒
b
3
[4]
2.
a
b
2
⇒
b
4
[2]
3.
b
2
a
⇒
b
4
[3]
4.
aba
⇒
b
[1]
# ab:aba=b,bbbb=abb b/a - - bbbbbbb=bbb abb=bbbb bba=bbbb aba=b