#4090 ⟨
a
,
b
|
aabaababa
=
ba
⟩
Up:
Monoids with two generators and one relation
Prev:
#4089
⟨
a
,
b
|
aabaababa
=
ab
⟩
Next:
#4091
⟨
a
,
b
|
aabaababa
=
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:
ba
=
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
ca
c
2
⇒
c
[4]
2.
ba
⇒
c
[2]
3.
bc
⇒ (
ca
)
2
c
2
[5]
# ab:aabaababa=ba ac/b ba=c magic:0 aacacc=c ba=c bc=cacacc