#13122 ⟨
a
,
b
|
aab
=
aaa
,
aba
=
ba
⟩
Up:
Monoids with two generators and two relations
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#13121
⟨
a
,
b
|
aab
=
aaa
,
aba
=
ab
⟩
Next:
#13123
⟨
a
,
b
|
aab
=
aaa
,
aba
=
bb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
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
4
[5]
2.
ba
⇒
a
4
[3]
3.
a
2
b
⇒
a
3
[1]
# ab:aab=aaa,aba=ba a/b aaaaa=aaaa ba=aaaa aab=aaa