#406 ⟨
a
,
b
,
c
|
abc
=
b
,
aca
=1⟩
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Monoid enumeration
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#405
⟨
a
,
b
,
c
|
abc
=
a
,
ccc
=1⟩
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#407
⟨
a
,
b
,
c
|
abc
=
b
,
acb
=1⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 7
Infinite non-commutative monoid
Element
a
has infinite order
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.
b
a
2
⇒
ab
[5]
2.
c
a
2
⇒ 1
[4]
3.
ac
⇒
ca
[3]
4.
bc
⇒
cab
[6]
# abc:abc=b,aca=1 ab/c - - baa=ab caa=1 ac=ca bc=cab