#12267 ⟨
a
,
b
|
aaab
=
ab
,
bbba
=
b
⟩
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Monoids with two generators and two relations
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#12266
⟨
a
,
b
|
aaab
=
ab
,
bbba
=
a
⟩
Next:
#12268
⟨
a
,
b
|
aaab
=
ab
,
bbbb
=
a
⟩
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 recursive path with deg(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
5
⇒
b
[7]
2.
ba
⇒
b
3
[8]
3.
a
3
b
⇒
ab
[1]
# ab:aaab=ab,bbba=b b/a bbbbb=b ba=bbb aaab=ab