#12149 ⟨
a
,
b
|
aaaa
=
aa
,
aaab
=
b
⟩
Up:
Monoids with two generators and two relations
Prev:
#12128
⟨
a
,
b
|
abba
=
bb
,
aaaaa
=1⟩
Next:
#12151
⟨
a
,
b
|
aaaa
=
aa
,
aaba
=
b
⟩
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.
ab
⇒
b
[4]
2.
a
4
⇒
a
2
[1]
# ab:aaaa=aa,aaab=b ab ab=b aaaa=aa