#14469 ⟨
a
,
b
|
aaab
=
a
,
bbbba
=
a
⟩
Up:
Monoids with two generators and two relations
Prev:
#14467
⟨
a
,
b
|
aaab
=
a
,
bbbab
=
a
⟩
Next:
#14472
⟨
a
,
b
|
aaab
=
a
,
bbbbb
=
b
⟩
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
9
⇒
a
[8]
2.
ab
⇒
a
7
[9]
3.
b
4
a
⇒
a
[2]
# ab:aaab=a,bbbba=a a/b aaaaaaaaa=a ab=aaaaaaa bbbba=a