#4856 ⟨
a
,
b
|
abbaaaab
=
abb
⟩
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Monoids with two generators and one relation
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#4855
⟨
a
,
b
|
abbaaaab
=
aba
⟩
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#4857
⟨
a
,
b
|
abbaaaab
=
baa
⟩
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
) = deg(
c
) = 0,
a
<
c
; deg(
b
) = 1
Auxiliary generators:
abb
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
cb
⇒
c
a
3
c
[5]
2.
c
a
4
b
⇒
c
[4]
3.
a
b
2
⇒
c
[2]
# ab:abbaaaab=abb ac/b abb=c magic:0 cb=caaac caaaab=c abb=c