#15008 ⟨
a
,
b
|
aaa
=
bb
,
bbbbbb
=1⟩
Up:
Monoids with two generators and two relations
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#14993
⟨
a
,
b
|
aaa
=
bb
,
ababbb
=1⟩
Next:
#15072
⟨
a
,
b
|
aab
=
aa
,
bbbbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-Abelian group
Inverses of generators:
a
-1
=
a
2
b
4
b
-1
=
b
5
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
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
⇒
b
2
[1]
2.
b
2
a
⇒
a
b
2
[3]
3.
b
6
⇒ 1
[2]
# ab:aaa=bb,bbbbbb=1 ab aaa=bb bba=abb bbbbbb=1