#3588 ⟨
a
,
b
,
c
|
ba
=
ac
,
bb
=
aa
⟩
Up:
Monoid enumeration
Prev:
#3587
⟨
a
,
b
,
c
|
ba
=
ab
,
cc
=
ab
⟩
Next:
#3590
⟨
a
,
b
,
c
|
ba
=
ac
,
bc
=
aa
⟩
Contents
Properties
Rewriting system
Properties
Sum of relation sides is 8
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
) = 0; deg(
b
) = deg(
c
) = 1,
b
<
c
Certificate
: derivations of all rewriting rules from the defining relations.
#
Rule
Proof
1.
a
2
b
⇒
b
a
2
[3]
2.
ac
⇒
ba
[1]
3.
b
2
⇒
a
2
[2]
# abc:ba=ac,bb=aa a/bc - - aab=baa ac=ba bb=aa