#5411 ⟨
a
,
b
|
aab
=
bb
,
bab
=
ab
⟩
Up:
Monoids with two generators and two relations
Prev:
#5410
⟨
a
,
b
|
aab
=
bb
,
bab
=
aa
⟩
Next:
#5412
⟨
a
,
b
|
aab
=
bb
,
bab
=
ba
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
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
2
b
⇒
b
2
[1]
2.
a
b
2
⇒
ab
[3]
3.
bab
⇒
ab
[2]
4.
b
3
⇒
b
2
[4]
# ab:aab=bb,bab=ab ab aab=bb abb=ab bab=ab bbb=bb