#5393 ⟨
a
,
b
|
abbaaab
=
bbaa
⟩
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Monoid enumeration
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#5392
⟨
a
,
b
|
abbaaab
=
babb
⟩
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#5394
⟨
a
,
b
|
abbaaab
=
bbab
⟩
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
|
aaabbab
-1
b
-1
a
-1
a
-1
b
⟩
Anti-isomorphic embedding:
φ
(
a
) =
a
,
φ
(
b
) =
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
Auxiliary generators:
c
=
bbaa
Reduction order:
Left-to-right shortlex with
a
<
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
acab
⇒
c
[4]
2.
b
2
a
2
⇒
c
[2]
3.
cb
a
2
⇒ (
ac
)
2
[6]
4.
c
2
ab
⇒
b
2
ac
[5]
# ab:abbaaab=bbaa abc bbaa=c magic:0 acab=c bbaa=c cbaa=acac ccab=bbac