#4444 ⟨
a
,
b
,
c
|
aba
=1,
bbbc
=
c
⟩
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Monoid enumeration
Prev:
#4423
⟨
a
,
b
,
c
|
aba
=1,
accc
=
c
⟩
Next:
#4447
⟨
a
,
b
,
c
|
aba
=1,
bbcb
=
c
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
Infinite non-cancellative non-commutative monoid
Element
a
has infinite order
Not right cancellative, because right multiplication by
c
is not injective:
b
3
⋅
c
=
c
and 1 ⋅
c
=
c
, however
b
3
≠ 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
Reduction order:
Left-to-right recursive path with deg(
b
) = deg(
c
) = 0,
b
<
c
; deg(
a
) = 1
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
b
3
c
⇒
c
[2]
2.
ba
⇒
ab
[3]
3.
a
2
b
⇒ 1
[4]
4.
a
2
c
⇒
b
2
c
[5]
# abc:aba=1,bbbc=c bc/a - - bbbc=c ba=ab aab=1 aac=bbc