#22822 ⟨
a
,
b
|
aaa
=1,
abbbb
=
bba
⟩
Up:
Monoids with two generators and two relations
Prev:
#22821
⟨
a
,
b
|
aaa
=1,
abbbb
=
bab
⟩
Next:
#22823
⟨
a
,
b
|
aaa
=1,
abbbb
=
bbb
⟩
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(
b
) = 0; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
16
⇒
b
2
[3]
2.
b
2
a
⇒
a
b
4
[2]
3.
a
3
⇒ 1
[1]
# ab:aaa=1,abbbb=bba b/a bbbbbbbbbbbbbbbb=bb bba=abbbb aaa=1