#6486 ⟨
a
,
b
|
aba
=
b
,
aaaaa
=
a
⟩
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Monoids with two generators and two relations
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#6485
⟨
a
,
b
|
aba
=
a
,
bbbbb
=
b
⟩
Next:
#6489
⟨
a
,
b
|
aba
=
b
,
aaaab
=
b
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
Infinite non-commutative monoid
Rewriting system
Format:
Pretty
Plain
Word to reduce:
Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Reduction strategy:
Leftmost
Rightmost
Path to normal form:
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
5
⇒
a
[2]
2.
b
a
4
⇒
b
[3]
3.
ab
⇒
b
a
3
[4]
# ab:aba=b,aaaaa=a a/b aaaaa=a baaaa=b ab=baaa