#7227 ⟨
a
,
b
,
c
|
aa
=1,
bacb
=
cb
⟩
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Monoid enumeration
Prev:
#7226
⟨
a
,
b
,
c
|
aa
=1,
bacb
=
ca
⟩
Next:
#7228
⟨
a
,
b
,
c
|
aa
=1,
bacb
=
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
d
is not injective:
ba
⋅
d
=
d
and 1 ⋅
d
=
d
, however
ba
≠ 1
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
Auxiliary generators:
d
=
cb
Reduction order:
Left-to-right recursive path with deg(
a
) = deg(
b
) = deg(
d
) = 0,
a
<
b
<
d
; deg(
c
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
Morphocompletion
: how the auxiliary generators were found.
#
Rule
Proof
1.
a
2
⇒ 1
[1]
2.
bad
⇒
d
[5]
3.
cb
⇒
d
[3]
4.
cd
⇒
dad
[6]
# abc:aa=1,bacb=cb abd/c cb=d morph:2/1 aa=1 bad=d cb=d cd=dad