#12001 ⟨
a
,
b
|
aabb
=
ba
,
aabab
=1⟩
Up:
Monoids with two generators and two relations
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#11985
⟨
a
,
b
|
aabb
=
ab
,
aabab
=1⟩
Next:
#12043
⟨
a
,
b
|
abab
=
aa
,
bbbbb
=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
2
b
2
⇒
ba
[1]
2.
a
(
ab
)
2
⇒ 1
[2]
# ab:aabb=ba,aabab=1 ab aabb=ba aabab=1