#27215 ⟨
a
,
b
|
aa
=1,
babbbab
=
bb
⟩
Up:
Monoid enumeration
Prev:
#27212
⟨
a
,
b
|
aa
=1,
babbabb
=
bb
⟩
Next:
#27219
⟨
a
,
b
|
aa
=1,
babbbbb
=
bb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-cancellative non-commutative monoid
Element
ba
has infinite order
Not left cancellative, because left multiplication by
b
is not injective:
b
⋅
a
b
3
ab
=
b
2
and
b
⋅
b
=
b
2
, however
a
b
3
ab
≠
b
Not right cancellative, because right multiplication by
b
is not injective:
ba
b
3
a
⋅
b
=
b
2
and
b
⋅
b
=
b
2
, however
ba
b
3
a
≠
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
Reduction order:
Left-to-right shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
b
4
ab
⇒
ba
b
4
[3]
3.
ba
b
3
ab
⇒
b
2
[2]
# ab:aa=1,babbbab=bb ab - - aa=1 bbbbab=babbbb babbbab=bb