#3205 ⟨
a
,
b
|
abaabaabbab
=1⟩
Up:
Monoids with two generators and one relation
Prev:
#3200
⟨
a
,
b
|
abaabaaaaab
=1⟩
Next:
#3210
⟨
a
,
b
|
abaabababba
=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
(
b
a
2
)
2
b
2
⇒ (
a
2
b
)
2
bab
[2]
2.
(
a
2
b
)
2
b
(
ab
)
2
⇒ 1
[3]
# ab:abaabaabbab=1 ab abaabaabb=aabaabbab aabaabbabab=1