#18616 ⟨
a
,
b
|
aba
=
b
,
aaaaaaa
=1⟩
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Monoid enumeration
Prev:
#18615
⟨
a
,
b
|
aba
=
a
,
bbbbbbb
=1⟩
Next:
#18619
⟨
a
,
b
|
aba
=
b
,
aaaaabb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 11
Infinite non-commutative monoid
Element
b
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
Reduction order:
Left-to-right recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
7
⇒ 1
[2]
2.
ab
⇒
b
a
6
[3]
# ab:aba=b,aaaaaaa=1 a/b - - aaaaaaa=1 ab=baaaaaa