#7209 ⟨
a
,
b
,
c
|
aa
=1,
babb
=
cb
⟩
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Monoid enumeration
Prev:
#7207
⟨
a
,
b
,
c
|
aa
=1,
babb
=
bc
⟩
Next:
#7210
⟨
a
,
b
,
c
|
aa
=1,
babb
=
cc
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
ab
has infinite order
Not right cancellative, because right multiplication by
b
is not injective:
c
⋅
b
=
ba
b
2
and
bab
⋅
b
=
ba
b
2
, however
c
≠
bab
Rewriting system
Format:
Pretty
Plain
Word:
Enter a word above to compute its normal form. Tips:
Lowercase letters stand for generators.
Spaces are ignored.
Numbers repeat the previous letter, e.g.
b90
.
Strategy:
Leftmost
Rightmost
Result:
1
1
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
b
) = 0,
a
<
b
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
cb
⇒
ba
b
2
[2]
# abc:aa=1,babb=cb ab/c - - aa=1 cb=babb