#15960 ⟨
a
,
b
|
aaa
=
aa
,
abab
=
aa
⟩
Up:
Monoids with two generators and two relations
Prev:
#15958
⟨
a
,
b
|
aaa
=
aa
,
aabb
=
ba
⟩
Next:
#15961
⟨
a
,
b
|
aaa
=
aa
,
abab
=
ab
⟩
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
3
⇒
a
2
[1]
2.
a
2
b
⇒
ab
a
2
[3]
3.
(
ab
)
2
⇒
a
2
[2]
# ab:aaa=aa,abab=aa a/b aaa=aa aab=abaa abab=aa