#3418 ⟨
a
,
b
|
aaaabbbaba
=
b
⟩
Up:
Monoid enumeration
Prev:
#3417
⟨
a
,
b
|
aaaabbbaba
=
a
⟩
Next:
#3419
⟨
a
,
b
|
aaaabbbabb
=
a
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite cancellative non-commutative monoid
Element
a
has infinite order
Submonoid of enveloping group: ⟨
a
,
b
|
aaaabab
-1
ab
-1
b
-1
b
-1
⟩
Anti-isomorphic embedding:
φ
(
a
) =
a
,
φ
(
b
) =
b
-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
Reduction order:
Left-to-right shortlex with
b
<
a
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
4
b
3
a
b
2
⇒
b
a
3
b
3
aba
[2]
2.
a
4
b
3
aba
⇒
b
[1]
# ab:aaaabbbaba=b ba - - aaaabbbabb=baaabbbaba aaaabbbaba=b