#3977 ⟨
a
,
b
|
abba
=
bb
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
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#3958
⟨
a
,
b
|
abba
=
aa
,
bbbb
=1⟩
Next:
#3979
⟨
a
,
b
|
abbb
=
ab
,
bbbb
=1⟩
Properties
Presentation has sum-of-sides 10
Infinite non-Abelian group
Inverses of generators:
a
-1
=
b
2
a
b
2
b
-1
=
b
3
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 shortlex with
a
<
b
a
b
2
a
⇒
b
2
b
4
⇒ 1
# ab:abba=bb,bbbb=1 ab abba=bb bbbb=1
Right Cayley graph (truncated)
Left Cayley graph (truncated)
