#2306 ⟨
a
,
b
|
abaabab
=
aab
⟩
Up:
Monoid enumeration
Prev:
#2305
⟨
a
,
b
|
abaabab
=
aaa
⟩
Next:
#2307
⟨
a
,
b
|
abaabab
=
aba
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 10
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not left cancellative, because left multiplication by
a
is not injective:
a
⋅
ba
(
ab
)
2
=
a
2
b
and
a
⋅
ab
=
a
2
b
, however
ba
(
ab
)
2
≠
ab
Not right cancellative, because right multiplication by
b
is not injective:
(
aba
)
2
⋅
b
=
a
2
b
and
a
2
⋅
b
=
a
2
b
, however (
aba
)
2
≠
a
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
Auxiliary generators:
c
=
aab
Reduction order:
Right-to-left recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
ac
⇒
c
2
ab
[5]
2.
ab
c
2
⇒
c
2
ab
[6]
3.
a
2
b
⇒
c
[2]
4.
abcab
⇒
c
[4]
# ab:abaabab=aab reversed:bc/a aab=c magic:0 ac=ccab abcc=ccab aab=c abcab=c