#4754 ⟨
a
,
b
|
abaaaaab
=
aab
⟩
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Monoids with two generators and one relation
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#4753
⟨
a
,
b
|
abaaaaab
=
aaa
⟩
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#4755
⟨
a
,
b
|
abaaaaab
=
aba
⟩
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
b
<
c
<
a
Auxiliary generators:
aaaaab
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
ac
⇒
c
2
[5]
2.
a
2
b
⇒
abc
[3]
3.
ab
c
4
⇒
c
[4]
# ab:abaaaaab=aab bca aaaaab=c morph:6/1 ac=cc aab=abc abcccc=c