#22807 ⟨
a
,
b
|
aaa
=1,
abbab
=
bab
⟩
Up:
Monoids with two generators and two relations
Prev:
#22801
⟨
a
,
b
|
aaa
=1,
ababb
=
bbb
⟩
Next:
#22808
⟨
a
,
b
|
aaa
=1,
abbab
=
bba
⟩
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(
a
) = 0; deg(
b
) = 1
a
3
⇒ 1
b
2
ab
⇒
a
(
ab
)
2
b
(
ab
)
2
⇒
bab
ba
(
ab
)
2
⇒ (
ab
)
2
# ab:aaa=1,abbab=bab a/b aaa=1 bbab=aabab babab=bab baabab=abab
Right Cayley graph (truncated)
Left Cayley graph (truncated)
