#10683 ⟨
a
,
b
|
aaab
=
aaa
,
bbbb
=1⟩
Up:
Monoids with two generators and two relations
Prev:
#10664
⟨
a
,
b
|
aaaa
=
bbb
,
abab
=1⟩
Next:
#10711
⟨
a
,
b
|
aaab
=
aba
,
bbbb
=1⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
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 shortlex with
a
<
b
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
3
b
⇒
a
3
[1]
2.
b
4
⇒ 1
[2]
# ab:aaab=aaa,bbbb=1 ab aaab=aaa bbbb=1