#22792 ⟨
a
,
b
|
aaa
=1,
ababa
=
bab
⟩
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Monoid enumeration
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#22787
⟨
a
,
b
|
aaa
=1,
abaab
=
bbb
⟩
Next:
#22793
⟨
a
,
b
|
aaa
=1,
ababa
=
bbb
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-commutative monoid
Element
b
a
2
has infinite order
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
=
bab
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
c
) = deg(
b
) = 1,
c
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
3
⇒ 1
[1]
2.
ac
⇒
c
a
2
[6]
3.
bc
⇒
caba
[8]
4.
bab
⇒
c
[3]
# ab:aaa=1,ababa=bab a/cb bab=c morph:3/0 aaa=1 ac=caa bc=caba bab=c