#4300 ⟨
a
,
b
|
ababababa
=
ab
⟩
Up:
Monoids with two generators and one relation
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#4299
⟨
a
,
b
|
ababababa
=
aa
⟩
Next:
#4301
⟨
a
,
b
|
ababababa
=
bb
⟩
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:
ab
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
c
4
a
⇒
c
[4]
2.
ab
⇒
c
[2]
3.
cb
⇒
c
5
[5]
# ab:ababababa=ab ac/b ab=c magic:0 cccca=c ab=c cb=ccccc