#12043 ⟨
a
,
b
|
abab
=
aa
,
bbbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#12001
⟨
a
,
b
|
aabb
=
ba
,
aabab
=1⟩
Next:
#12047
⟨
a
,
b
|
abab
=
ab
,
aaabb
=1⟩
Properties
Presentation has sum-of-sides 11
Infinite non-commutative monoid
Complete 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(
b
) = 0; deg(
a
) = 1
b
5
⇒ 1
aba
⇒
a
2
b
4
a
2
b
4
a
⇒
a
3
b
a
3
b
2
a
⇒
a
4
b
3
a
4
b
3
a
⇒
a
5
b
2
# ab:abab=aa,bbbbb=1 b/a bbbbb=1 aba=aabbbb aabbbba=aaab aaabba=aaaabbb aaaabbba=aaaaabb
Right Cayley graph (truncated)
Left Cayley graph (truncated)
