#5333 ⟨
a
,
b
|
aaa
=
ab
,
bba
=
ba
⟩
Up:
Monoids with two generators and two relations
Prev:
#5332
⟨
a
,
b
|
aaa
=
ab
,
bba
=
ab
⟩
Next:
#5334
⟨
a
,
b
|
aaa
=
ab
,
bba
=
bb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 10
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.
a
6
⇒
a
4
[3]
2.
ab
⇒
a
3
[1]
3.
b
2
a
⇒
ba
[2]
# ab:aaa=ab,bba=ba a/b aaaaaa=aaaa ab=aaa bba=ba