#5903 ⟨
a
,
b
|
ababba
=
bbaba
⟩
Up:
Monoids with two generators and one relation
Prev:
#5902
⟨
a
,
b
|
ababba
=
bbaab
⟩
Next:
#5904
⟨
a
,
b
|
ababba
=
bbabb
⟩
Quick links
Properties
Rewriting system
Properties
Presentation has sum-of-sides 11
Infinite non-cancellative non-commutative monoid
Not right cancellative, because right multiplication by
a
is not injective:
aba
b
2
⋅
a
=
b
(
ba
)
2
and
b
2
ab
⋅
a
=
b
(
ba
)
2
, however
aba
b
2
≠
b
2
ab
Enveloping group: ⟨
a
,
b
|
aabba
-1
b
-1
⟩
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:
Right-to-left recursive path with deg(
a
) = 0; deg(
b
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
(
ba
)
2
⇒
aba
b
2
a
[1]
# ab:ababba=bbaba reversed:a/b bbaba=ababba