#3867 ⟨
a
,
b
|
aaaaabaaa
=
bb
⟩
Up:
Monoids with two generators and one relation
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#3866
⟨
a
,
b
|
aaaaabaaa
=
ba
⟩
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#3868
⟨
a
,
b
|
aaaaabaab
=
aa
⟩
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(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
2
⇒
a
5
b
a
3
[1]
2.
a
5
b
a
3
b
⇒
b
a
5
b
a
3
[2]
# ab:aaaaabaaa=bb a/b bb=aaaaabaaa aaaaabaaab=baaaaabaaa