#6818 ⟨
a
,
b
|
aab
=
b
,
abb
=
aaa
⟩
Up:
Monoids with two generators and two relations
Prev:
#6797
⟨
a
,
b
|
aba
=
b
,
bbbb
=
bb
⟩
Next:
#6821
⟨
a
,
b
|
aab
=
b
,
bab
=
aaa
⟩
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
3
[6]
2.
b
a
2
⇒
b
[8]
3.
a
2
b
⇒
b
[1]
4.
b
2
⇒
a
4
[3]
# ab:aab=b,abb=aaa a/b aaaaa=aaa baa=b aab=b bb=aaaa